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Jearl Walker 

g Circus of Physics 



The flying circus of physics 


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flying circus of physics 

John Wiley & Sons 




ASS t^o. 

530.010 WAU 

5 OCT 1978 

Copyright © 1975, 1977 by John Wiley & Sons, Inc. 

All rights reserved. Published simultaneously in Canada. 

No part of this book may be reproduced by any means, nor 
transmitted, nor translated into a machine language with- 
out the written permission of the publisher. 

Library of Congress Cataloging in Publication Data: 

Walker, Jeari, 1945- 

The flying circus of Physics. 


1. Physics-Problems, exercises, etc. 

I. Title. 

QC32,W2 530 75-5670 

ISBN 0-471 -02984-x^/ 

Printed in the United States of America 
10 9876543 

for elizabeth 


These problems are for fun. I never meant them to be taken 
too seriously. Some you will find easy enough to answer. 
Others are enormously difficult, and grown men and women 
make their livings trying to answer them. But even these 
tough ones are for fun. I am not so interested in how many 
you can answer as I am in getting you to worry over them. 

What I mainly want to show here is that physics is not some- 
thing that has to be done in a physics building. Physics and 
physics problems are in the real, everyday world that we live, 
work, love, and die in. And I hope that this book will capture 
you enough that you begin to find your own flying circus of 
physics in your own world. If you start thinking about phys- 
ics when you are cooking, flying, or just lazing next to a 
stream, then I will feel the book was worthwhile. Please let me 
know what physics you do find, along with any corrections or 
comments on the book.* However, please take all this as being 
just for fun. 

Jearl Walker 

My grandmother's house 
Aledo, Texas, 1977 

*Physics Department, Cleveland State University, Cleveland, Ohio 441 15. 


I should in no way give the impression that this book was written by me 
alone. Lots of people contributed, helped, argued, criticized, encour- 
aged, and understood. Since I was a graduate student at the University 
of Maryland when I wrote the book, I must thank Howard Laster and 
Harry Kriemelmeyer for their willingness to support a graduate student 
with such an offbeat idea. Dick Berg, also at Maryland, contributed 
many ideas and hours of discussion. Sherman Poultney not only gave 
me several good problems but also was understanding when my disserta- 
tion occasionally (frequently) fell victim to my book. My wife, 
Elizabeth, typed and edited the manuscript. Art West, who was also a 
graduate student at the time, gave very valuable and detailed sugges- 
tions on the semifinal version. However, it was Joanne Murray who 
toiled through my morass of the English language and read and edited 
many versions of the manuscript. I am especially indebted to her. I 
also thank Don Deneck, Edwin Taylor, George Arfken, Ralph Llewellyn, 
and A. A, Strassenburg who thoughtfully read the manuscript and 
offered many very valuable suggestions. 

Jearl Walker 

1 Hiding under the covers, 
listening for the monsters 


1.1 Squealing chalk 3 

1.2 A finger on the wine glass 

1.3 Two-headed drum 
vibrations 3 

1.4 Bass pressed into records 

1.5 Whistling sand 3 

1.6 Booming sand dunes 3 

1.7 Chladni figures 4 

1.8 Pickin' the banjo and 
fingering the harp 4 

1.9 String telephone 4 

1.10 Bowing a violin 4 

1.11 Plucking a rubber band 

1.12 The sounds of boiling 
water 5 

1.13 Murmuring brook 5 

1.14 Walking in the snow 5 

1.15 Silence after a snowfall 5 

1.16 Ripping cloth 5 

1.17 Knuckle cracking 6 

1.18 Snap, crackle, and pop 6 

1.19 Noise of melting ice 6 

1.20 An ear to the ground 6 

1.21 Voice pitch and helium 6 

1.22 Tapping coffee cup 6 

1.23 Orchestra warmup and 
pitch changes 7 

1.24 Bending to the ground to 
hear an airplane 7 

1.25 Culvert whistlers 7 

1.26 Music hall acoustics 7 

1.27 Acoustics of a 
confessional 7 
























Sound travel on a cool 
day 8 

Silent zones of an 
explosion 8 
Echoes 8 

The mysterious whispering 
gallery 9 

Musical echoes 10 

Tornado sounds 10 

Echo Bridge 10 

Sound travel in wind 11 

Brontides 11 

Shadowing a seagull's cry 

Lightning without thunder 

Submarine lurking in the 
shadows 12 

Cracking a door against 
the noise 12 
Feedback ringing 12 
Foghorns 13 

Whispering around a head 

End effects on open- 
ended pipes 13 
Getting sick from 
infrasound 13 
Noisy water pipes 13 
Piles and ripples of a 
Kundttube 14 
Pouring water from a 
bottle 14 
Seashell roar 14 

Talking and whispering 

Shower singing 15 

A shattering singer 15 

Howling wind 15 

Twirl-a-tune 15 

Whistling wires 16 


1.56 The whistling teapot 16 

1.57 Blowing on a Coke bottle 

1.58 Police whistle 17 

1.59 Whistling through your 
lips 17 

1.60 Gramophone horns 17 

1.61 Vortex whistle 17 

1 .62 Sizes of woofers and 
tweeters 17 

1.63 The cheerleading horn 18 

1.64 Bass from small speakers 

1.65 Screams of race cars and 
artillery shells 18 

1.66 Bat sonar 18 

1.67 Hearing Brownian motion 

1 .68 When the cops stop the 
party 1 9 

1 .69 V-2 rocket sounds 1 9 

1.70 Cocktail party effect 19 

1.71 Taping your voice 19 

1.72 Fixing the direction of a 
sound 20 

1.73 Sonic booms 20 

1 .74 Sounds of thunder 20 

1.75 Hearing aurora and frozen 
words 20 

1.76 Dark shadows on clouds 

1.77 Whip crack 21 

2 The walrus speaks of 
classical mechanics 22 

2.1 Run or walk in the rain? 

2.2 Catching a fly ball 23 

2.3 Running a yellow light 

2.4 Getting the bat there in 
time 23 

2.5 Turn or stop 24 

2.6 The secret of the golf 
swing 24 

2.7 Jumping beans 24 

2.8 Jumping 24 

2.9 Throwing the Babe a slow 
one 25 

2.10 Karate punch 25 

2.11 Hammers 25 

2.12 Softballs and hardballs 

2.13 Heavy bats 25 

2.14 Jerking chair 25 

2.15 Click beetle's somersault 

2.16 The weight of time 26 

2.17 Pressure regulator 26 

2.18 The superball as a deadly 
weapon 27 

2.19 Locking brakes 27 

2.20 Wide slicks on cars 27 

2.21 Friction in drag racing 

2.22 Sliding stick across fingers 

2.23 Accelerating and braking 
in a turn 28 

2.24 Starting a car 28 

2.25 Left on the ice 28 

2.26 Turning a car, bike, and 
train 29 

2.27 Pool shots 29 

2.28 Superball tricks 30 

2.29 Bike design 30 

2.30 Hula-Hoop 31 

2.31 Keeping a bike upright 

2.32 Cowboy rope tricks 31 

2.33 Spinning a book 31 

2.34 Fiddlesticks 32 

2.35 Eskimo roll 32 

2.36 Large diameter tires 32 

2.37 Car in icy skid 32 

2.38 Tire balancing 32 

2.39 Tearing toilet paper 32 

2.40 Skipping rocks 33 

2.41 Car differential 34 

2.42 Racing car engine mount 

2.43 Tightrope walk 34 

2.44 Carnival bottle swing 34 

2.45 Falling cat 34 

2.46 Ski turns 34 

2.47 Yo-yo 35 

2.48 Slapping the mat in judo 

2.49 Bullet spin and drift 35 

2.50 The leaning tower of 
books 35 

2.51 Falling chimneys 36 

2.52 The Falkland Islands 
battle and Big Bertha 36 

2.53 Beer's law of river erosion 

2.54 A new twist on the 
twirling ice skater 36 

2.55 Boomerangs 37 

2.56 Swinging 37 

2.57 Soldiers marching across 
footbridge 37 

2.58 Incense swing 38 

2.59 Road corrugation 38 

2.60 A ship's antiroll tank 39 

2.61 Inverted pendulum, 
unicycle riders 39 

2.62 Spring pendulum 39 


The bell that wouldn't 


Blow-holes 47 


Freezing water 55 

ring 40 


Decompression schedule 


Freezing hot and cold 


Swinging watches 40 


water 55 


Earth vibrations near 


Hot water turning itself 


Worldwide thunderstorm 

waterfalls 40 

off 48 

activity 56 


Stinging hands from 


Bursting pipes 48 


Getting stuck by the cold 

hitting the ball 40 


Fever thermometer 49 



The archer's paradox 40 


Heating a rubber band 49 


Wrapping ice 56 


Magic windmill 41 


Watch speed 49 


Pond freeze 56 


Personalities of tops 42 


U-tube oscillations 49 


Skiing 56 


Diabolos 42 


Bike pump heating up 50 


Ice skating 57 


Spinning eggs 42 


West-slope hill growth 


Snow avalanche 57 


The rebellious celts 42 



Making a snowball 57 


Tippy tops 43 


The Chinook and going 


Snow tires and sand for 


Seeing only one side of 
moon 43 


mad 50 
Coke fog 51 


ice 58 
Salting ice 58 


Spy satellites over Moscow 


Convertible cooling effect 


Antifreeze coolant 58 




Feeling cool while wet 


Moon trip figure 8 44 


Death Valley 51 



Earth and sun pull on 


Mountain top coldness 


Carburetor icing 58 

moon 44 



Eating polar ice 59 


Making a map of India 44 


Holding a cloud together 


A pan top for boiling 


Air drag speeds up 


water 59 

satellite 44 


Mushroom clouds 51 


Briefly opening oven 59 



Holes in the clouds 51 
Mountain clouds 52 
Spherical cloud of A- 
bomb blast 52 
Burning off clouds 52 
Mamma 53 




Water tub saving the 
vegetables 59 
Icehouse orientation 59 
Heating meat with a 
"Sizzle Stik" 60 
The highest mountain 60 

3 Heat fantasies and other 
cheap thrills of the night 45 


The well-built stewardess 


Making cakes at high 
altitudes 46 

The Swiss cottage baro- 
meter 46 


Cause of fog 53 
Breath condensation 53 
Contrails and distrails 53 
Salt water bubbles 53 



The boiling water ordeal 

Boiling point of water 60 
A puddle's salt ring 61 


Wells and storms 46 


Fireplace draft 54 


Dunking bird 61 


One balloon blowing up 
another balloon 46 

Champagne recompression 



Open-air fires 54 

Cigarette smoke stream 


Stack plumes 55 



Dancing drops on hot 
skillet 62 
Geysers 62 
Percolator 63 


Emergency ascent 47 


Shades of ice coverings 


Single-pipe radiators 63 


Licking a red-hot steel 


A warm blanket of snow 


Measuring blood pressure 

bar 63 




Banging radiator pipes 64 


Fires from A-bombs 71 


Last lock in Panama 77 


Wrapping food with 


Growing crystals 71 


Panama Canal ocean levels 

aluminum foil 64 


Snowflake symmetry 71 


Old incandescent bulb 6 A 


Two attractive Cheerios 


Hourglass's bouyancy 77 


How hot is red hot? 64 



Boat sinking in pool 77 


Cool room with 


Cultivating farmland 71 


Coiled water hose 78 

refrigerator 64 


Wall curvatures of a liquid 


Floating ship in dry dock 


Black pie pans 65 

surface 72 



Archimedes's death ray 


Rising sap in trees 72 


Submarine stability 78 



Ice columns growing in 


Floating bar orientation 


Toy putt-putt boat 65 

ground 72 



Feeling cold objects 65 


Growing stones in the 


Fish ascent, descent 79 


White clothes in the tropics 

garden 72 


Inverted water glass 79 



Winter buckling of roads 


Floating bodies 79 


Cast-iron cookery 66 



Stability of an inverted 


The season lag 66 


Shorting out a masonry 

glass of water 79 


Temperature of space walk 

wall 73 


The perpetual salt 



Soap bubbles 73 

fountain 79 


Greenhouse 67 


Inverted soap bubbles 74 


Salt fingers 80 


Why do you feel cold? 


A candle's flickering 


Salt oscillator 80 


death 74 


Narrowing of falling water 


Wrapping steam pipes 68 


Dust explosion 74 

stream 80 


Thunderstorm wind 


Davy mine lamps 74 


Beachball in an air stream 

direction 68 


Mud polygons and drying 



Silvery waves from your 

cracks 75 


Toy with suspended ball 

finger 68 


Thermal ground cracks 



Insect plumes over trees 



Ball balanced on a water 



Stone nets 75 

jet 81 


Shrimp plumes and Ferris 


Life and the Second Law 


Egg pulled up by water 

wheel rides 69 




Heat stroke 69 
CooHng a coffee 70 


Spoon in a faucet stream 

4 The madness of stirring tea 


Polariod color 



Water tube spray guns 82 

development 70 
Heat islands 70 


Passing trains 82 



Holding back the North 


Ventilator tops and prairie 


Total kinetic energy in a 

Sea 77 

dog holes 82 

heated room 70 


Breathing through air tube 


Insects rupturing on 


Smudge pots in the 


windshields 83 

orchard 71 


Flapping flags 83 


Wings and fans on racing 


Ekman spiral 93 


Parachute holes 101 

cars 83 


Stronger ocean currents 


Speed of a drifting boat 


Lifting an airplane 84 

in the west 94 



Pulling out of nose dive 


Tea leaves 94 


The gaps in snow fences 



River meander 94 



Sailing into the wind 84 


Rising ball in rotating 


Snowdrifts 101 


Frisbee 84 

water 94 


Streamlined airplane wings 


Manpowered flight 85 


Taylor's ink walls 95 



Golf ball top spin 85 
Flettner's strange ship 85 
Winds through a building 


Bathtub vortex 95 
Tornadoes and water 
spouts 95 


Skiing aerodynamics 102 
Dimpled golf balls 102 
Flight of the plucked bird 



Soda water tornado 95 



Curve, drop, and knuckle 


Coffee cup vortex 95 


Bird soaring 103 

balls 86 


Dust devils 95 


Kites 103 


Curves with smooth balls 


Fire vortices 96 


Cloud streets 103 



Steam devil 96 


Coffee laced with polygons 


Building waves 86 


Vortex rings from falling 



Monster ocean waves 86 

drops 96 


Longitudinal sand dune 


Whitecaps 87 


Ghost wakes 96 

streets 1 04 


Boat speed and 


Hot and cold air vortex 


Smoke ring tricks 105 

hydroplaning 87 

tube 97 


Sand ripples 105 


Whirligig beetle waves 


Birds flying in V formation 


Siphons 106 




Marching sand dunes 106 


Ship waves 88 


Sinking coin 97 


TheCrapper 106 


Edge waves 88 


Tailgating race cars 97 


Street oil stains 107 


Swing of waves to shore 


Several sinking objects 


Lake surface lines 107 


interacting 98 


Milk's clear band 107 


Surf skimmer 89 


Stange air bubbles in 


Spreading olive oil on 


Surfing 89 

water 98 

water 107 


Bow-riding porpoises 89 


Fish schooling 99 


Marine organic streaks 


Ocean tides 90 


Wind gusts on building 



Tides: sun versus moon 



Splashing milk drops 108 



Tacoma Narrows Bridge 


Water bells 108 


Tidal friction effects 90 
Seiches 91 
Tidal bores 91 


collapse 99 

Air turbulence 100 

Watch speed on a mountain 


Water sheets 109 
Gluing water streams 


Bay of Fundy tide 92 
Sink hydraulic jump 93 


top 100 

Wire mesh on faucet 100 


Pepper and soap 109 
Pouring from a can 109 


Standing waves in falling 


Fast swimming pools 


Nappe oscillations 100 


Tears of whiskey 1 1 


stream 93 
Beach cusps 93 



Aquaplaning cars 110 
Floating water drops 1 1 


Soup swirl reversal 110 


Flattened sun and moon 


Sky polarization 127 


A leaping liquid 110 
Rod-climbing egg whites 



Blue ribbon on sea horizon 



Colored frost flowers 

Cellphane between two 


Liquid rope coils 1 1 1 
Thixotropic margarine 


30° reflection off the sea 


Lunar light triangles 120 


polarizing filters 127 
Spots on rear window 


Die-swelling Silly Putty 


Shiny black cloth 120 


Optical activity of Karo 



Inverted shadows 121 

syrup 128 


Bouncing putty 1 12 


Pinhole camera 121 


Animal navigation by 


Self-siphoning fluids 112 
Quicksand 112 


Eclipse leaf shadows 121 
Heiligenschein 121 


polarized light 128 
Magic sun stones 129 


Unmixing a dye solution 


Bike reflectors 121 
Brown spots on leaves 


Haidinger's brush 129 
Sunset colors 129 
The blue sky 130 

5 She comes in colors 


Rays around your head's 


Twilight purple light 130 

everywhere 114 

shadow 122 


Zenith blue enhancement 


Cats' eyes in the dark 1 22 



Swimming goggles 1 1 5 
The invisible man 1 15 
Playing with a pencil in 
the tub 115 



Brightness of falling rain 


Rainbow colors 122 

Pure reds in rainbows 123 



Belt of Venus 130 
Green street lights and red 
Christmas trees 130 
Brightness of daytime sky 


Coin's image in water 


Distance of a fish 116 


Supernumerary bows 123 
Dark sky between bows 



Yellow ski goggles 131 

Stars seen through shafts 


Ghosting in double-walled 
windows 116 


Rainbow polarization 123 
Lunar rainbows 123 



Colors of lakes and oceans 


Mountain looming 116 
Fata Morgana 116 


Rainbow distance 123 
Rainbow pillar 123 



Color of overcast sky 


Seeing the dark part of the 

moon 131 

White clouds 131 

Sunlight scattered by 

clouds 131 


Oasis mirage 117 
Wall mirage 117 
Paper doll mirage 118 
One-way mirrors 118 
Red moon during lunar 


Reflected rainbows 124 
Dewbows 1 24 
Sun dogs 124 
The 22° halo 125 
Fogbows 125 




eclipse 118 
Ghost mirage 118 
Number of images in two 


Sun pillars 125 

Other arcs and halos 126 

Crown flash 127 


Maps in the sky 132 
Mother-of-pearl clouds 


mirrors 119 

The green flash 119 


Polarization for car lights 


Young's dusty mirror 


Bouncing a light beam 


Polarized glasses and glare 


Searchlight beams 133 


Zodiacal light and 


Lights through a screen 


Color effects from 

gegenschein 133 


fluorescent lights 148 


Windshield light streaks 


Star color 140 


Floating TV pictures 148 



Luminous tornado 140 


3-D movies, cards, and 


Color of a city haze 1 34 


Sugar glow 140 

posters 1 48 


Glory 134 


Suntans and sunburns 


Enlarging the moon 149 


Corona 135 



Rays of Buddha 149 


Frosty glass corona 135 


Fireflies 141 


Moon-to-sun line 149 


Bishop's Ring 135 


Other luminescent 


Bent search beams 150 


Streetl ight corona 1 35 

organisms 141 


Rear lights and a red 


Blue moons 135 


Photosensitive sunglasses 

light 150 


Yellow fog lights 135 



Snowblindness 150 


Blue hazes 136 


Black-light posters 142 


Resolution of earth objects 


Shadows in muddy water 


Fluorescent light 

by astronauts 1 50 


conversion 142 


A Christmas ball's 


Color of milk in water 


Speckle patterns 142 

reflection 150 



Humming and vision 142 


Moire patterns 151 


Color of cigarette smoke 


Sunglasses and motion 


distortion 143 

6 The electrician's evil and the 


Color of campf ire smoke 


Top patterns before TV 


ng's magic 1 52 



Oil slick and soap film 


screen 143 

A stargazer's eye jump 


Electrocution 153 

colors 136 



Color effects after 


Retinal blue arcs 143 


Frog legs 153 

swimming 136 


Phosphenes 144 


Getting stuck to electric 


Liquid crystals 137 


Streetlamp sequence 144 


wire 153 
Electric eel 153 


Butterfly colors 137 


Spots before your eyes 


Dark lines in a fork 137 



M icrowave cook i ng 1 54 


Eye floaters 137 


Purkinje's shadow figures 


Time to turn on light 


Points on a star 137 



Poisson spot 138 


Early morning shadows in 


Shocking walk on rug 


Kelvin water dropper 1 54 


Eclipse shadow bands 


your eyes 145 

Purkinje color effect 145 



Sunset shadow bands 


Mach bands 146 


Electrical field and water 
streams 155 



Seeing the colors of your 


Bands around a lake's 

mind 147 


Snow charging wire fences 

reflection 138 


Making colors with a finger 



Scotch tape glow 155 


Star twinkle 138 


Bleaching by light 139 


Colors in a black and 


Sifting sugar 155 

white disc 147 


Gas truck chains 155 


Optical levitation 139 


Charge in shower 155 


Happiness and negative 


Rain gush after lightning 

7.16 X rays in the art museum 

charge 155 




Fall through the floor 


Clothes thrown off 164 

7.17 Nuclear-blast fireball 173 



Ground fields in lightning 

7.18 Defensive shields in Dune 


Sand castles and crumbs 

hit 164 




St. Elmo's fire 165 

7.19 Friction 173 


Food wrap 156 


Living through lightning 

7.20 The flowing roof 173 


Magnetic-field dollar bill 


7.21 Cracks 174 



Bubbles moved by 

magnetic field 156 

Electromagnetic levitation 



Andes glow 165 
Electrical pinwheel 165 
Power-line blues 166 

7.22 Chrome corrosion 174 

7.23 Polishing 174 

7.24 Sticky fingers 174 
Bibliography 176 


Turning in the shade of a 
magnetic field 156 

7 The walrus has his last say 
and leaves us assorted goodies 

Index 219 
Answers 225 


Car speedometer 157 

Perpetual magnetic motion 



UFO propulsion 168 



Radio, TV reception 
range 157 
Crystal radio 158 
Airplane interference with 




Violating the virgin sky 


Olber's paradox 169 

Noctilucent clouds 169 

TV 158 


Water witching 170 


AM car antenna 158 


Snow waves 170 


Multiple stations on radio 


Fixed-point theorem 170 



The great leap downward 


Auroral displays 158 



Whistlers 160 


Beating and heating egg 


Lightning 160 

whites 171 


Earth's field 160 


Pulling off Scotch tape 


Lightning forms 161 
Ball lightning 161 



Footprints in the sand 


Balloon filled with water 

and sand 172 

Buying a sack of corn 



H-bomb lightning 162 
Volcanic lightning 162 
Earthquake lightning 162 
Franklin's kite 162 



Lightning rod 163 


Radiation levels in an 


Lightning and trees 163 

airplane 172 


Lightning strikes to aircraft 


Flashes seen by astronauts 

The flying circus of physics 


Hiding under 

the covers, 

listening for the monsters 


coupled oscillations 




Two-headed drum vibrations 

If a two-headed drum, such as the 
Indian tom-tom, is struck on one 
head, both heads will oscillate 
although they may not both be 
oscillating at any given instant. 
Apparently the oscillation is fed 
from one to the other, and each 
periodically almost ceases to move. 
Why does this happen? Wouldn't 
you have guessed that the mem- 
branes would oscillate in sympathy? 
What determines the frequency 
with which the energy is fed back 
and forth? 

124, p. 149; 126, p. 474. 




Whistling sand 

In various parts of the world, such 
as on some English beaches, there 
are sands that whistle when they 
are walked on. A scraping sound 
seems plausible, but I can't imagine 
what would cause a whistle. Do 
the sand grains have some unique 
shape so that the sand resonates? 

81, p. 145; 144, Chapter 17; 
145, p. 140; 146 through 150; 


Squealing chalk 

Why does a piece of chalk produce 
a hideous squeal if you hold it in- 
correctly? Why does the orienta- 
tion of the chalk matter, and what 
determines the pitch you hear? 

Why do squeaky doors squeak? 
Why do tires squeal on a car that 
is drag racing from a dead stop? 

/ through 3*. 







Booming sand dunes 

Even more curious is the 
"booming" occasionally heard 
from sand dunes. Suddenly, 
in the quiet of the desert, a dune 
begins to boom so furiously that 
one might have to shout to be 
heard by his companions. The 
clue to this may lie in the ac- 
companying avalanche on the 
leeward (downwind) side of the 
dune. Then again, there is nothing 
unusual about such avalanches for 
that is precisely how the dune it- 
self flows across the desert floor. 
Under some conditions could one 
of these avalanches cause a large 
vibration of the sand and thus 
produce the booming? 

144, Chapter 17; 146; 150. 

harmonic motion 


A finger on the wine glass 

Why does a wine glass sing when 
you draw a wet finger around its 
edge? What exactly excites the 
glass, and why should the finger be 
wet and greaseless? What deter- 
mines the pitch? Is the vibration 
of the rim longitudinal or trans- 
verse? Finally, why does the 
wine show an antinode** in its 
vibrational pattern 45° behind your 

124, p. 154. 

Exceptionally good references: Weather 
(a journal), Jones (82), Bragg (159). 
*The numbers following the problems 
refer to the bibliography at the end of 
the book. 

**An antinode is where the vibrational 
motion is maximum. 


Bass pressed into records 

If I turn down the volume on my 
record player and just listen to the 
sound coming directly from the 
stylus, I can hear high frequencies 
whenever they occur in the music, 
but there is almost no bass. Am- 
plifiers take this weaker bass into 
account and amplify the low fre- 
quencies much more than the 
high. Is there any practical reason 
for reducing the strength of the 
bass pressed into records? 


Hiding under the covers, listening for monsters 3 


standing waves 


Chladni figures 

Chladni figures are made with a 
metal disc supported at its center 
and sprinkled with sand. As a 
bowstring is drawn across an edge, 
the sand jumps into some geomet- 
ric design on the plate (Figure 
1.7). Why? Nothing to it, you 
say? It is just simple standing 
waves set up on the plate by the 
bowing? Well, then tell me why, 

using the same bowing motion, 
you get one design with sand and 
another design with a finer dust? 
You can even mix them up before- 
hand; they'll separate into their 
own designs as you bow the plate. 

81, pp. 129-131; 82, pp. 172- 
180; 124, pp. 61-62; 127, pp. 
172-176; 128, pp. 130-131; 
130 through 138; 139, p. 207; 
141, pp. 178-190; 142, pp. 88- 
91; 1529; 1551. 

Figure 1.7 

Bowing a plate to get Chladni figures. (Some of these may require the 

support of the plate in places other than the center.) 

string vibration 


Pickin' the banjo and fingering the 

Why does the banjo produce a 
twangy sound and the harp a soft 
mellow sound? One difference 
between the two instruments is 
that the banjo is plucked with 
a pick but the harp is plucked with 
a finger. How does this make 
a difference? 

82, pp. 283 ff; 128, pp. 92-93; 
145, p. 89. 

string vibration 



String telephone 

How does the string telephone that 
you played with as a child work? 
How does the pitch heard in the 
receiving can depend on the tight- 
ness and density of the string and 
the size of the can? Approximately 
how much more energy is transmit- 
ted with the string telephone than 
without it? 

82, pp. 103-104. 

string vibration 



Bowing a violin 

Plucking a string, as a guitar 
player does, seems a straightfor- 
ward way to excite vibrations in it. 

4 The flying circus of physics 

But how does the apparently 
smooth motion of bowing excite 
the vibrations of a violin string? 
Does the sound's pitch depend on 
the pressure or speed of the bowing? 

82, pp. 219-221, 291-300; 124, 
pp. 98 ff; 126, pp. 453-456; 127, 
pp. 101-103; 128, pp. 93-94; 
145, pp. 89-99; 151, pp. 90-93; 
152, pp. 167-170; 153; 1552. 

string vibration 


Plucking a rubber band 

If you tighten a guitar string, you 
raise its pitch. What happens if 
you do the same with a rubber 
band stretched between thumb 
and forefinger? Does its pitch 
change when it is stretched 
farther? No, the pitch remains 
fairly unchanged; or, if it does 
change, it becomes lower rather 
than higher. Why is there a dif- 
ference between rubber bands and 
guitar strings? 

154; 155, pp. 186-187. 


phase change 


The sounds of boiling water 

When I heat water for coffee, the 
sound of the water tells me when 
it has begun to boil. First there is 
a hissing that grows and then dies 
out as a harsher sound takes over. 
Just as the water begins really to 
boil, the sound becomes softer. 
Can you explain these sounds, 
especially the softening as the 
water begins to boil? 

157; 158, p. 295; 159, pp. 88- 
89; 160, p. 168. 



Murmuring brook 

At some time in your life you've 
probably spent a sunny afternoon 
lying in the grass, listening to 
the murmur of a brook. Why do 
brooks murmur? Why do water- 
falls and cataracts roar? 

What is responsible for the 
spritely sound of a just-opened 
soft drink? Look into a clear 
soft drink and try correlating 
the noise with the creation, move- 
ment, or bursting of the bubbles. 

145, p. 140; 159, pp. 129-130; 
161 through 163. 


phase change 


Walking in the snow 

Sometimes snow crackles when 
you walk in it, but only when the 
temperature is far enough below 
freezing. What causes the noise, 
and why does its production 
depend on the temperature? At 
approximately what temperature 
will the snow begin to crackle? 

164, p. 440; 165, p. 144; 166. 



Silence after a snowfall 

Why is it so quiet just after a snow- 
fall? There aren't as many people 
and cars outside as usual, but that 
alone doesn't explain such quiet- 
ness. Where does the energy of 
the outdoor noise go? Why does 
the snow have to be fresh? 

A similar sound reduction occurs 
in freshly dug snow tunnels in 
Antarctic expeditions: the 
speakers must shout to be heard 
if they are more than 1 5 feet 
apart. Again, what happens to 
the sound energy? 

165, p. 134; 167. 


Ripping cloth 

Why is it that when you tear a 
piece of cloth faster, the pitch of 
the ripping is higher? 

Hiding under the covers, listening for monsters 5 

7i v.- 

Figure 1.18 

"Listen. There it is again. 


Knuckle cracking 

What makes the cracking sound 
when you crack your knuckles? 
Why must you wait a while before 
you can get that cracking again? 



Snap, crackle, and pop 

Why exactly do Rice Krispies* 
go "snap, crackle, and pop" when 
you pour in the milk? 


Noise of melting ice 

Plop an ice cube or two into your 
favorite drink, and you'll hear 
first a cracking and then a 
"frying" sound. What causes these 
noises? Actually, not all ice will 

*A breakfast cereal from the Kellogg 

'Snap, crackle, pop. 

produce the "frying" sound. Why 
is that? 

Icebergs melting in their south- 
ward drift also make frying noises 
that can be heard by submarine 
and ship crews. The sound is called 
"bergy seltzer." 


acoustic conduction 


An ear to the ground 

Why did Indian scouts in the old 
Westerns fall to their knees and 
press their ears against the ground 
to detect distant, and unseen, 
riders? If they could hear the 
distant pounding of hooves 
through the ground, why couldn't 
they hear it through the air? 

124, p. 21. 



Voice pitch and helium 

When people inhale helium gas, 
why dues the pitch of their voices 

One should be very, very 
cautious in inhaling helium. One 
can suffocate with the helium 
while feeling no discomfort be- 
cause there is no carbon dioxide 
accumulation in the lungs. Never, 
never inhale hydrogen or pure 
oxygen. Hydrogen is explosive 
and oxygen supports burning. 
Even a spark from your clothes 
can lead to death. 

170, p. 219; 171, pp. 16-17. 

speed of sound 


Tapping coffee cup 

As you stir instant cream or in- 
stant coffee into a cup of water, 
tap the side with your spoon. The 
pitch of the tapping changes 
radically as the powder is added 
and then during the stirring. Why? 

Tap the side of a glass of beer 
as the head goes down. Again, the 
pitch changes. Why? 

You may have a tendency to 
answer that the foam or the powder 
damp the oscillations caused by 
the tapping, but even if that is true, 
would that change the pitch or 
only the amplitude? 

159, p. 158; 173. 

6 The flying circus of physics 

speed of sound 
and temperature 


Orchestra warmup and pitch 

Why does the pitch of the wind 
instruments increase as an orchestra 
warms up? Why does the pitch of 
the string instruments decrease? 

124, pp. 49-50; 126, p. 498; 



Bending to the ground to hear an 

I have read that if I put my head 
close to the ground while listening 
to an airplane fly by, the pitch of 
the airplane's noise may seem to 
increase. Similarly, if I stand by 
a wall near a waterfall, I may hear, 
in addition to the normal sound 
of the waterfall, a softer back- 
ground sound. The closer I stand 
to the wall, the higher the pitch of 
the extra sound. In either case, 
why would I hear a sound 
whose pitch depends on the near- 
ness of my ear to the solid struc- 

82, pp. 98-100; 145, p. 59; 174 
through 180. 




Culvert whistlers 

Stand in front of a long concrete 
culvert and clap you hands sharply. 
You will hear not only the echo 
of your clap, but also a "zroom," 
which starts at a high pitch and 
drops to a low pitch within a 
fraction of a second.* What's 
responsible for the "zroom"? 

181; 182. 


Music hall acoustics 

Why are concert halls generally 
narrow with high ceilings? If 
echoes are undesirable shouldn't 
the walls and ceiling be close to 
the listener? That way the 
listener will not be able to distin- 
guish the direct sound from the 
reflected sound. What is the 
minimum time difference between 
two sounds that the listener can, 
in fact, distinguish? Why does 
a hall full of people sound much 
better than an empty hall? 

If echoes are to be eliminated, 
why aren't the walls and ceilings 
covered with material that will 
absorb the sound? Granted that 
the hall's beauty might be de- 
stroyed, it still appears that halls 
are designed so as not to elimin- 
ate all sound reflections. In fact, 
the walls and ceilings may be 

*Crawford (181) has described these as 
being analogous to atmospheric whistlers 
(see Prob. 6.31). 

covered with nooks and cran- 
nies that reflect the sound in 
every which way. On the other 
hand, a hall with no reflections 
is said to be acoustically dead. 

124, Chapter 13; 127, pp. 531- 
540; 128, Chapter 10; 142, 
Chapter 14; 145, pp. 279-293; 
152, Chapter 9; 158, pp. 609- 
616; 170, pp. 265-266; 171, 
pp. 44-50; 183, pp. 123-180; 
184, Chapter 14; 185, Chapter 
11; 186, Chapter 8; 187, pp. 
291-300; 188 through 195; 1528. 




Acoustics of a confessional 

Some rooms are especially noted 
for their strange acoustics; some 
even provide a focusing of the 
sound. Such focusing was ap- 
parently used in the "Ear of 
Dionysius" in the dungeons of 
Syracuse where the acoustics 
somehow fed words and even 
whispers of the prisoners into a 
concealed tube to be heard by the 

For an example in recent times, 
the dome covering the old Hall of 
Representatives in the Capitol 
building (Washington, D.C.) would 
reflect even a whisper from one 
side of the chamber in such a way 
that it would be audible on the 
opposite side. More than once 
this was rumored to have em- 
barrassed representatives whispering 
party secrets to their colleagues. 

The Cathedral of Girgenti in 

Hiding under the covers, listening for monsters 1 

Sicily provided even more severe 
embarassment. Its shape is that of 
an ellipsoid of revolution, so thee 
sound produced at one focus of 
the ellipsoid is nearly as loud at 
the other focus. Soon after it was 
built one focus was unknowingly 
chosen for the position of the 
The focus was discovered by 
accident, and for some time 
the person who discovered 
it took pleasure in hearing, 
and in bringing his friends 
to hear, utterances in- 
tended for the priest 
alone. One day, it is said, 
his own wife occupied 
the penitential stool, and 
both he and his friends were 
thus made acquainted with 
secrets which were the 
reverse of amusing to one 
of the party (141). 

139, p. 194; 141, p. 48; 197, 
Chapter 11. 




Sound travel on a cool day 

Why does sound travel farther on a 
cool day than on a warm day? This 
is especially noticeable over calm 
water or a frozen lake. The range 
of sounds in the desert, on the 
other hand, may be noticeably 

81, pp. 34-35; 82, p. 107; 
124, p. 17; 127, pp. 322-325; 
142, pp. 117-118; 185, pp. 


Silent zones of an explosion 

During World War II it was often 
noticed that as one would drive 
toward a distant artillery piece, 
the roar of its fire would disap- 
pear at certain distances (Figure 
1.29). Why were there such 
silent zones? 

Sound travel over large distances 
is also curious. For example, 

during World War I people on the 
English shore could hear gunfire 
from installations in France. What 
conditions permit such an enormous 
sound range? 

150; 165, pp. 135 ff; 187, p. 137; 
214, p. 2; 215, pp. 23-25; 216; 
217, pp. 9- 14; 218; 2 19, pp. 
291-293; 313, pp. 71 ff. 



, *:~5-> ■, 

, *%>>> :; 

x : : * ? Artillery in center. : >>>' 

5v^ : T - White areas indicate ->-;*;- 

■■:-% €t % r -; where explosion canf : : >^ 

'" !*..' .. *...^f!.i...*!J ' *» fctA Imia***! i..^^!*"» .*>.. 

Figure 1.29 

309-311; 186, pp. 66-67; 187, 
p. 137; 207, pp. 50-52; 209, 
pp. 24-25; 210, p. 600; 21 1, 
pp. 474-475; 212; 213, pp. 49- 


Rayleigh scattering 



I am sure you can explain echoes- 
they are reflections of the sound 
waves by some distant object, 
right? Then explain why some 
echoes return to the speaker with 

a higher pitch than that of the 
initial sound. Also, why does a 
high-pitched sound usually pro- 
duce a louder, more distinct 
echo than a low-pitched sound? 
How close to the reflecting 
wall can you stand and still hear 
an echo? 

81, p. 31; 82, pp. 86-87; 127, 
pp. 311-313; 142, p. 132; 164, 
p. 426; 182; 198, pp. 147-154; 

8 The flying circus of physics 

Rayleigh waves 

intensity and distance 



The mysterious whispering gallery 

It was Rayleigh who first explained 
the mysterious whispering gallery 
in the dome of London's St. Paul's 
Cathedral. In this large gallery 
there is a peculiar audibility for 
whispers. For instance, if a friend 
were to whisper to the wall some- 
where around the gallery, you 
would be able to hear his whisper 
no matter where you might stand 
along the gallery (Figure 1.31a). 
Strangely enough, you will hear 
him better the more he faces the 
wall and the closer he is to it. 

Is this just a straightforward re- 
flection and focusing problem? 
Rayleigh made a large model of 
the gallery to find out. He placed 
a birdcall at one point along the 
model gallery and a flame at 
another point. When sound waves 
from the birdcall impinged on the 
flame, the flame would flare, and 
so the flame was his sound detec- 
tor. You are probably tempted 
to draw the sound rays shown in 
Figure 1.31/?. But before you 

Figure 1.31b 

Rayleigh 's model of whispering 

gallery. Birdcall causes flame to 


Figure 1.31a 

Cutaway view of whispering 


Figure 1.31c 

With thin screen placed near the 

wall, birdcall cannot make flame 


put too much faith in them, sup- 
pose a narrow screen were to be 
placed at some intermediate point 
along the inside perimeter of the 
metal sheet (as shown in Figure 
1.31c, but exactly where along 

the perimeter doesn't matter). If 
your idea about the rays is correct, 
the flame should still flare be- 
cause the screen is out of the way, 
right? Well, as a matter of fact, 
when Rayleigh inserted a screen, 
the flame did not flare. The 
screen must somehow have blocked 
the sound waves. But how? After 
all, it was only a narrow screen 
placed seemingly well out of the 
way of the sound rays. This result 
gave Rayleigh a clue to the nature 
of the whispering gallery. 

81, pp. 32-33; 82, pp. 87-92; 
127, pp. 315-316; 198, pp. 126- 
129; 199 through 205. 

Hiding under the covers, listening for monsters 9 



Musical echoes 

What causes the musical echo you 
can sometimes hear when you 
make a noise near a fence or a 
flight of stairs? Can you calculate 
the pitch of the echo? 

81, p. 32; 127, pp. 313-314; 
145, p. 13; 164, pp. 426-427; 
182; 206; 207, pp. 47-48; 208. 




Tornado sounds 

My grandmother could always 
forecast a tornado by the 
deathly silence that would sud- 
denly fall before the appearance 
of the tornado. Why the silence? 
When the twister hit, there would 
be a deafening roar much like a 
jet plane's. Why the roar? Finally, 
there are reports that in the 
tornado's center it is, again, deathly 
quiet. Can this be true? Wouldn't 
you hear at least the furious de- 
struction taking place outside the 

165, pp. 144-145; 223, pp. 67, 
83; 224 through 226. 


Rayleigh waves 


Echo Bridge 

The whispering gallery effect may 
be responsible for some of the 
sounds you can hear beneath a 
bridge arch. If you stand near the 
wall of such an arch (Figure 1.34) 
and whisper faintly, you will hear 
two echoes; a loud handclap will 

yield many echoes. Can you ac- 
count for these echoes? They can 
result either from normal reflec- 
tions off the water or from the 
whispering gallery effect, or from 

82, p. 87; 202; 203. 

Figure 1.34 
Echo bridge. 

wWm&i I J 

10 The flying circus of physics 



Sound travel in wind 

Why is it easier to hear a distant 
friend yell if you are downwind 
rather than upwind? Is it because, 
as is commonly thought, there is a 
greater attenuation in the upwind 

81 , pp. 33-34; 82, pp. 107- 
108; 124, pp. 17-18; 127, 
pp. 322-325; 142, pp. 119- 
121; 185, pp. 11-13,311; 186, 
pp. 66-67; 187, p. 137; 207, 
pp. 52-53; 210, pp. 599-600; 
212; 213, pp. 52-55; 222. 




Throughout history there have 
been tales of mysterious sounds 
from the sky, rumblings, and short 
cracklings when the sky is per- 
fectly clear and there are no 
obvious noise sources. These 
noises— called brontides, mist- 
poeffers, or Barisal guns— are 
heard virtually everywhere: over 
flatland, over water, and in the 
mountains. In a study of 200 
Dutch mistpoeffers it was found 
that the sound came most often 
in the morning and afternoon, less 
often at noon, and hardly ever 
during the night. In some places 
they are far from rare. For ex- 
ample, near the Bay of Bengal 
they are heard so frequently that 

the people ascribe the sounds to 
the gods. In other places, how- 
ever, they are now probably dis- 
missed as sonic booms. 

One is tempted to identify these 
mysterious sounds as distant 
thunder, but thunder is normally 
not heard at distances greater 
than 15 miles*. Besides, these 
sounds are heard on clear days. 

Can you think of other possible 

164, p. 442; 227; 161 1, Section 

*SeeProb. 1.38 



Shadowing a seagull's cry 

For an example of quiet "shadows' 
behind objects, let me offer the 
following story (see Figure 1.37). 
In the spring the seagulls resort 
in large numbers to the moss 
to lay their eggs and when the 
young birds are able to fly, 
the air is filled with their 
shrill screams. There is a road 
at a little distance from the 
nests and by the side of the 
road there is sometimes a row 
of stacks of peat. The length 
of one of these stacks is many 
times as great as the wave- 

length of the scream of the 
birds and consequently a good 
sound shadow is formed. Op- 
posite the gap between two 
stacks the sound is unpleasant- 
ly loud; opposite the stack it- 
self there is almost complete 
silence, and the change from 
sound to silence is quite sud- 
den (234). 
Would there be a quiet region if 
seagulls cried in a deep voice rather 
than their shrill one? 

128, p. 18; 234, p. 103. 



Figure 1.37 

Hiding under the covers, listening for monsters 1 1 



Lightning without thunder 

Often a lightning stroke appears 
unaccompanied by thunder. In 
fact, thunder is rarely heard beyond 
about 15 miles from the lightning 
flash. Why? Is 15 miles really such 
a great distance for sound to travel? 
No, artillery fire and explosions 
can certainly be heard beyond 15 
miles. Why not thunder as well? 

82, pp. 1 14- 1 16; 142, p. 1 18; 
164, pp. 44 1-442; 219, pp. 304- 
305; 220, p. 196; 221. 



Cracking a door against the noise 

If I close my door, which leads 
to a very noisy hall, my room is 
kept quiet. If I open the door 
wide, though, it is hard to think 
with all the noise. How about 
cracking the door just a little? 
That certainly should be almost 
the same as closing it all the way. 
Yet, I try it and discover the noise 
to be almost as bad as with the 
door wide open. Why does even a 
small crack make such a dispro- 
portionate difference in the noise 
level of my room? 

128, p. 19; 155, p. 177. 


Feedback ringing 

There was an era in rock and roll 
when feedback was used extensive- 
ly to give a psychedelic quality to 
the music. A guitar player would 
play facing into his own speaker, 
and the speaker output would be 
picked up and reamplified by his 
electric guitar. That same type of 
ringing can be heard if a radio 
announcer holds a radio tuned to 
his own station near his micro- 
phone. In either case what causes 
the ringing? 



Submarine lurking in the shadows 

Though sonar systems are powerful a sonar unit and a sub at about the detected. What causes those 
enough to detect submarines at same depth (Figure 1.39). For shadows? 

very large distances, they are usually some reason other than just absorp 

limited to only several thousand 
meters (in the tropics to even less 
than that). Consider, for example, 

tion, sound radiated toward the sub 
never reaches it; the sub is said to 
be in a shadow area and won't be 

171, pp. 86-89; 185, p. 235; 
2 17, pp. 16- 19; 228, pp. 376- 
379; 229 through 232. 


Figure 1.39 

12 The flying circus of physics 




Foghorns should be designed to 
spread their sound over a wide 
horizontal field, wasting as little 
as possible upward. Doesn't it 
seem strange, then, that rectangu- 
lar foghorns are oriented with 
the long sides of their openings 
vertical (Figure 1.42). Isn't that 
orientation precisely the wrong 

142, pp. 124-125; 145, p. 
167; 159, pp. 159-160; 235, 
pp. 78-79; 236. 

Figure 1. 42 



Whispering around a head 

You can hear a friend's normal 
voice reasonably well whether he 
is facing you or turned away. 
Why is it that you can hear his 
whisper only if he is facing you, 

even if the whisper is as loud as 
his normal voice? 

159, pp. 85-86; 198, p. 127; 
237, p. 188; 238, pp. 47-48; 
239, p. 220. 


End effects on open-ended pipes 

Why is there an antinode of air 
movement (and a node of pres- 
sure) at each end of an open pipe 
when standing sound waves are 
set up inside? Since there is a 
node at a closed end, there should 
be an antinode at an open end, 
right? Can you actually show 
why there is an antinode there? 
As a matter of fact, the antinode 
is not precisely at the open end, 
and where it really is depends on 
several parameters of the pipe 
(width, for example). Will this 
departure from simple theory 
effect the practical use of pipes 
in such things as organs? 

82, pp. 136-139; 126, pp. 
493-496; 127, pp. 181-182; 
145, pp. 163-165; 240; 241. 

resonant oscillation 


Getting sick from infrasound 

Infrasound (sound of a subaudible 
frequency) can make you nauseous 
and dizzy. . . it can even kill you. 
Now that its danger is being re- 

cognized, infrasound is being dis- 
covered in many common set- 
tings: near aircraft, in cars at high 
speeds, near ocean surfs, in thunder- 
storms, and near tornados, for 
example. It may even warn 
animals and some especially sensi- 
tive people of an impending 
earthquake. Why does infrasound 
affect people and animals this 
way? In particular, how can it 
cause such things as internal 

171, pp. 139-147; 1489 
through 1491; 1534 through 



Noisy water pipes 

Why do the pipes sometimes groan 
and grumble when I turn on and 
off my water faucet? Why doesn't 
it happen all the time? Where 
exactly does the noise originate: 
in the faucet, the pipe immediate- 
ly behind it, or a turn in the pipe 
somewhere down the line? Why is 
there rumbling only with certain 
flow rates? Finally, why can the 
problem be alleviated by adding a 
vertical pipe of trapped air to the 
water pipe? 

183, p. 46; 251; 252. 

Hiding under the covers, listening for monsters 13 


vortex motion 



Figure 1.47a 

The dust is left in piles and ripples when the rod is stroked. 



Piles and ripples of a Kundt tube 

The Kundt tube has long been a 
simple demonstration of acoustic 
standing waves, but can you really 
explain how it works? It consists 
of a long glass tube containing 
some light powder (cork dust or 
lycopodium powder, for example). 
The tube is corked at one end 
and sealed at the other with a 
brass rod (Figure 1.47a). When 
the rod is stroked with a rosin- 
coated chamois, not only does the 
rod squeal, but also the dust in the 
tube collects in periodic piles along 
the tube. Standing sound waves 
must do this to the dust, but how? 
Moreover, if one of the piles of 

Figure 1.47b 

With a loudspeaker as an exciter, 
thin discs of dust form across the 
tube's cross section. 

powder is examined closely, it is 
found to contain a series of ripples. 
If standing waves make the piles, 
what makes the ripples? 

If the rod is replaced by a pure 
tone loudspeaker, discs form in 
between the piles (Figure 1.47b). 
Each disc resembles a very thin 
barrier extending across the tube. 
What generates them? 

82, pp. 208-214; 124, pp. 113- 
114; 127, pp. 188-191,255-258, 
472; 128, pp. 22-23; 130; 141, 
pp. 244-253; 145, pp. 220-222; 
207, pp. 151-156; 243 through 
250; 1517. 


Pouring water from a bottle 

As water is poured from a bottle, 
the pitch of the pouring noise 
decreases. As water is poured back 
in, the opposite change in pitch 
occurs. Why? 


Seashell roar 

What causes the ocean roar that 
you hear in a seashell? 

82, pp. 196-197; 141, pp. 253- 
254; 150; 238, pp. 57-58, 65. 




Talking and whispering 

What determines the pitch of your 
voice? Why are women's voices 
higher than men's? Many young 
men go through a stage in which 
their voices change. What causes 
that? How do you switch from a 
normal voice to a whisper? 

81, pp. 113-114; 124, pp. 75-77, 
132-136; 127, pp. 207-211; 141, 
pp. 238-244; 142, pp. 179-1 SI- 
MS, pp. 254-255; 151, pp. 175- 
177; 238, Chapter 7; 239; 
253, p. 387; 254. 

14 The flying circus of physics 


Shower singing 

Why does your singing sound so 
much richer and fuller in the 
shower (Figure 1.51)? 


A shattering singer 

Champagne glasses can be shattered 
by opera singers who sing at some 
high pitch with great power. Why 
does the glass shatter, and why 
must a particular pitch be sung? 
Why does it take several seconds 
before the glass shatters? 


Howling wind 

Monster movies always have a 
howling wind as a background 

sound to the sinister deeds of the 
monster. How does wind howl? 

150; 164, pp. 442-443. 


Bernoulli effect 



A musical toy called "Twirl-a- 
tune"* is a surprisingly simple 
toy: it's nothing but a flexible, 
corrugated plastic tube made 
much like a vacuum cleaner hose 
and open at both ends. When 
held by one end and whirled about 
(Figure 1.54), it produces a 
musical tone. At higher speeds, 
you get higher pitched tones; the 
transition from pitch to pitch is 
not smooth but takes place in 
jumps. A gathering of many 
twirlers can produce quite a 

Figure 1.51 

Figure 1.54 

sound, and the fairies in a partic- 
ular English presentation of 
A Midsummer Night's Dream even 
gave a chorus of such twirling 
tubes to enhance their magic 
(1588). How are the tones made, 
and why are the pitch changes 

The tendency will be to dismiss 
the questions by pointing to the 
standard textbook example of 
sound resonance in open-ended 
pipes. But here you will first have 
to understand why there is any 
sound at all and why the sound's 
frequency range depends on the 
whirling speed. Also, you should 
figure out which way the air moves 
through the tube. Only then can 
you use the textbook explanation 
of why only certain frequencies 
will be stored and built up inside 
the tube. 

Will the centrifugal force on the 
tube affect the frequency of the 


*Avalon Industries, Inc., 95 Lorimer 
St, Brooklyn, New York 1 1206; see 
Ref. 1588 for other trade names. 

Hiding under the covers 15 

vortex formation 


Whistling wires 

Why do telephone wires whistle 
in the wind? Why did the aeo- 
lian harps of ancient Greece sing 
when left in the wind? In partic- 
ular, do the wires or strings them- 
selves have to move in order to 
produce the sound? If they 
move, do they move in the plane 
of the wind or perpendicular to 
it? What determines the pitch you 

Suppose you were to simulate 
the wind whistling through tele- 
phone wires by waving a fork with 
long, thin prongs. Which way 
would you wave it, in the plane of 
the prongs or perpendicular to that 
plane? Try it both ways. 

What causes the sighing of trees 
in winter and the murmur of an 
entire forest? Do all trees sigh at 
the same pitch? 

82, pp. 304-313; 124, pp. 114- 
116; 126, pp. 480-482; 127, 
pp. 218-220; 142, p. 215; 145, 
pp. 149-152; 150; 155, pp. 188- 
189; 164, pp. 443-448; 165, 
p. 144; 207, pp. 156-157; 256, 
pp. 126-128; 257, pp. 123-130; 
258 through 261. 

sound from vortices 



The whistling teapot 

Other types of whistles use an 
obstruction in the way of the air 
stream. For example, an edge 
tone can be produced by direct- 
ing an air stream onto a wedge 
(Figure 1.56a). Similarly, a 
ring tone is made by placing a ring 
in the stream path (Figure 1.566). 
The most familiar of all is the 
common teapot whistle that has 
a hole in the stream's way and 
that produces what is called a 
hole tone (Figure 1.56c). In each 
example the whistling sound de- 
pends on the obstructing object, 
but how? What really produces the 
whistling you hear when your tea- 
pot boils? 

124, pp. 1 16 ff; 126, pp. 482-485; 
127, pp. 220-223; 142, p. 216; 
145, pp. 169-174; 151, pp. 95- 
97; 257, pp. 130-138; 258; 263 
through 269. 


Figure 1.56a 
Edge- tone setup. 

Figure 1.56b 
Ring- tone setup. 

Figure 1.56c 
Hole- tone setup. 


sound from vortices 


Blowing on a Coke bottle 

Making a Coke bottle hum by 
blowing across its opening is an 
example of still another type of 
whistle. Not only is there an ob- 
struction, the edge of the bottle, 
but there is also a cavity adjacent 
to the obstruction. Flutes, record- 
ers, and organ pipes are other 

examples of the same kind of 

Why do such devices produce 
particular frequencies? In other 
words, how do the fingering of 
holes on the cavity (as in the case 
of the flute) and the change of air 
pressure across the obstruction 
determine the different frequenc- 
ies that can be made? In the case 
of the Coke bottle, does the 
bottle's mouth size affect the 
frequency? How about shape? 
Suppose I partially fill a bottle 

16 The flying circus off physics 

with water, excite it with tuning 
forks to find its resonant frequency, 
and then tilt the bottle. The in- 
ternal shape changes, of course, 
but does the resonant frequency? 

142, p. 163; 151, pp. 95-97; 
159, pp. 74-75; 170, pp. 218- 
219; 258; 310; 1553. 


Police whistle 

How does an American police 
whistle work? As above, there is 
an edge across which air is blown 
and there is an adjacent cavity. 
There is also a small ball in that 
cavity. What does the ball do for 
the whistling? Why won't the 
whistle work underwater? 



Whistling through your lips 

Finally we come to the most 
common whistle of them all, 
although perhaps the most difficult 
to explain: whistling through your 
lips. What's responsible for this 
sound? Can you whistle under- 

82; 258. 


Gramophone horns 

Remember the old gramophones 
with their cranks and big horns? 

Why did they haye horns? Did the 
horns concentrate sound in a cer- 
tain direction? Why did they use 
an expanding horn and not just a 
straight tube? The point was that 
if the sound box's diaphragm 
coupled directly to the room's air 
without the intervening horn, 
there was poor sound emission. 
What can an expanding horn do in 
coupling the sound box with the 

124, pp. 212-214; 186, pp. 208- 


acoustic impedance 



Sizes of woofers and tweeters 

Why is the woofer (low frequency 
speaker) so much larger than the 
tweeter (high frequency speaker) 
in most hi-fi systems? 

128, p. 148; 187, pp. 272-273, 
280; 228, pp. 174-175. 

sound from vortices 


Vortex whistle 

The vortex whistle (Figure 1.61) 
produces sound when you blow 
through a tube that juts out from 
a round cavity. Apparently vor- 
tices are set up in the cavity and, 
when they emerge from a central 
hole, a whistling sound is made. 
Unlike the common "police 
whistle," the vortex whistle pro- 

Blow in here f 

duces a frequency that depends 
on the pressure with which the 
whistle is blown. Hence, by vary- 
ing the pressure, you can play 
tunes on it. What produces the 
whistling sound, and why does 
the frequency depend on the pres- 

258; 262. 


! i! 111! Sound emer 8* s her « 

Figure 1.61 

Vortex whistle (after Bernard Vonnegut, J. Acoustical Soc. Amer., 

26, 18 (1954). 

Hiding under the covers, listening for monsters 17 

spherical and plane waves 

400-402; 128, pp. 31-32, 56- 
59; 151, pp. 1 17- 120; 152, pp. 
105-108; 170, pp. 40-42; 184, 
pp. 403-406; 209, pp. 179- 
187; 228, pp. 253-256; 237, 
pp. 66-68; 256, pp. 231-245; 
270, pp. 129-133; 271, pp. 50- 
52; 272, Chapter 7, pp. 4 1 1- 
413; 273 through 279. 

thus finding the distance to a 
reflecting object? Does it detect 
the Doppler shift (frequency shift) 
if either it or the object is moving? 
Or does it locate the object by 
triangulation of the return sound, 
much as we perceive depth with 
binocular vision? Maybe it is 
even more complicated because 
some bats chirp, that is, each sound 
pulse sweeps from about 20 kHz 
down to 15 kHz. How can such a 
chirp be used to extract more in- 
formation about the object? 

What is the smallest insect that 
a bat can detect using a constant 
frequency pulse of 20 kHz? 

142, pp. 353-354; 280 through 
284; 1493 through 1497. 

intensity versus range 



The cheerleading horn 

How does a cheerleader's horn 
make the yell louder in one direc- 
tion? Do multiple reflections in- 
side the horn limit the direction 
of spreading? This may seem 
reasonable, but considering the 
size of the horn compared to 
the wavelengths of the sound, 
how can there possibly be such 
a concentrating effect due to in- 
ternal reflections? So, again, 
why is the yell louder in the direc- 
tion of the horn? 

127, pp. 205-207; 142, p. 1 1 1; 
145, pp. 239-240; 159, pp. 12- 
13; 213, p. 47; 235, p. 78; 242. 

Doppler shift 


Screams of race cars,artillery 

Why does the pitch of a race 
car's scream change as the car 
speeds past you? Surely the noise 
thrown forward is no different 
from that thrown backward. 
On the battlefield men can 
predict the danger of an incoming 
shell by the scream it makes. 
Not only do they listen for the 
change in loudness but also the 
pitch and its change. What does 
the pitch tell them? 

128, p. 19. 

Brownian motion 



Hearing Brownian motion 

Hearing involves detection of air 
pressure variations, right? Well, 
the air next to the eardrum is con- 
tinually fluctuating in pressure. 
How large are those fluctuations on 
the ear drum, and are they large 
enough to be heard? If they are, 
then why don't you hear them? 
Shouldn't there be a continuous 
roar in your ears? 


combination tones 

nonlinear response 


Bass from small speakers 

Isn't it surprising that telephones, 
high fidelity earphones, and small 
transistor radios can reproduce 
bass (see Prob. 162)? The speakers 
in them are so small, yet one does 
hear bass from them. The horns 
on early gramophones shouldn't 
have been able to handle low 
frequencies either. In both cases, 
why is bass heard? 

82, pp. 256-261; 124, pp. 29- 
32, 84-87, 165, 2 14; 127, pp. 

Doppler shift 



Bat sonar 

To find their way and to locate 
insects, most bats emit a high fre- 
quency sound and then detect the 
echo. What does a bat actually 
do with the echo? Does it emit 
a sound pulse and time its return, 

18 The flying circus of physics 

acoustic power 

shock wave 


signal-to- noise ratio 


When the cops stop the party 

Some cocktail parties are quiet; 
others are loud. Can you roughly 
calculate the critical number of 
guests beyond which the party be- 
comes loud? You might take the 
transition point as when the back- 
ground noise on your listener be- 
comes as great as your volume on 

Suppose the guests are called to 
attention by the hostess, and then, 
afterwards, allowed to resume their 
conversations. About how much 
time will pass before the party be- 
comes loud again? 



V-2 rocket sounds 

If you were being fired on with 
artillery shells, you would first 
hear the shell's scream, then its 
explosion, and finally the roar of 
the gun. But in the V-2 rocket 
attacks on London during World 
War II, the first two sounds came 
in reverse sequence: first the 
explosion, and slightly later the 
rocket's whine. Why the difference? 

142, p. 153. 



Htm the. 



Cocktail party effect 

How can you distinguish the 
words of one person when there is 
a lot of background noise? If you 
tape a friend talking to you at a 
loud party, it's likely that on tape 
you won't be able to hear him at 
all, much less understand the 
words. Why the difference? 

171, p. 62; 238, pp. 15- 16; 286. 

acoustic conduction 



Taping your voice 

If you've ever taped your own 
voice, you were probably sur- 
prised by how thin it sounded 
when you played it back. Other 
people recorded their voice and 
their playbacks sounded fine to 
you. But yours. . .it just wasn't 
right. What was wrong? 


Hiding under the covers, listening for monsters 19 

acoustic conduction 

shock wave 



% 18 




1 12 



1 6 

50 100 200 300 500 1000 2000 3000 5000 10,000 
Frequency (Hz) 

Figure 1. 72 

[From Konishi (Ref. 1554) after Steven and Newman (Ref. 1555).] 


Fixing the direction of a sound 

Since you have two ears instead 
of one, you can locate the direc- 
tion of a sound as well as just hear 
the sound. If you were to plot 
your ability to fix the direction of 
a pure tone versus the frequency 
of that tone, you would find that 
your ability is reasonably constant 

with frequency except in the re- 
gion of 2 to 4 kHz (Figure 1.72). 
Why does your ability get worse 
in that particular region, whereas 
it is better for both higher and 
lower frequency tones? 

1554; 1555. 

shock waves 



Sonic booms 

What causes the sonic booms 
produced by supersonic aircraft? 
Is the boom produced only when 
the plane first breaks the sound 
barrier? Does it depend on the 
engine noise? Sometimes you 
hear not just one boom but two 
right in succession. Why two? 

Why not always two? Does the 
boom depend on the aircraft's 
altitude? Does it matter if the 
plane is climbing, diving, or 
turning? Under some circum- 
stances the aircraft may generate 
a "superboom"— an especially in- 
tense shock wave. Under other 
conditions a boom will be made by 
the plane but will never reach the 
ground. What probably happens to 

288 through 298. 


Sounds of thunder 

When I was little my mother told 
me that thunder had something to 
do with lightning. How is thunder 
produced, and why does it last for 
such a relatively long time? Must 
it always boom? I've read that if 
you stand within 1 00 yards of the 
lightning flash you first hear a 
click, then a crack (as in a whip 
crack), and finally the rumbling. 
What causes the click and the 
crack? If you're a little further 
away you'll hear a swish instead 
of the sharp click? Why a swish? 

82, pp. 1 14- 1 16; 220, Chapter 6, 
pp. 195-199; 299, pp. 124-127; 
300, pp. 162- 163; 30 1, pp. 66- 
67; 302 through 305; 1617. 

sound propagation 



Hearing aurora and frozen words 

Is it possible to hear aurora*? 
There have been reports of 
cracklings or swishings (sounding 
like "burning grass and spray") 
coordinated with changes in the 
light intensity of aurora. While 
it is hard to imagine how sound 
made at such a high altitude (above 
70 km) could reach an observer on 
the ground with any appreciable 
power simply because of the at- 

20 The flying circus of physics 

tenuation over such a large distance, 
recently an explanation along 
this line was proposed: electrons 
from the aurora would excite 
what are called plasma acoustic 
waves that would create normal 
acoustic waves. Regardless of the 
actual mechanism, however, could 
you hear a sound made so high? 
What exactly happens to the 
acoustic power when the sound 
travels downward through the 

Another interesting explanation 
has been that "What one hears is 
one's own breath that freezes in 
the cold air" (Figure 1.75). When 
the air is calm and very cold, can 
you actually hear the collision of 
ice crystals formed from your 
breath? If this is ever possible, how 
cold must it be? 

1506 through 151 1; 1532. 

*See Prob. 6.30. 

Figure 1. 75 

shock waves 


Dark shadows on clouds 

During the fighting near the 
Siegfried Line in World War II, 
U. S. troops spotted dark shadows 
crossing over white cirrus clouds. 
These shadows were arcs whose 
centers lay on the German side, 
supposedly being caused by the 
heavy artillery. Why were these 
shadows produced? Would you 
expect the shadows to come 
singly or always in pairs? Finally, 
was the cloud background necessary? 

142, p. 154; 306 through 308. 


Whip crack 

What makes the sound when a whip 
is cracked? Try to support any 
guess with rough numbers. 

82, p. 30; 159, p. 184; 288; 

Hiding under the covers, listening for monsters 21 

The walrus speaks 
of classical mechanics 


equation of motion 






cross sectipn 


Linear kinematics 
and dynamics 

2.1 to 2.22 


Run or walk in the rain 

Should you run or walk when 
you have to cross the street in the 
rain without an umbrella? Running 
means spending less time in the 
rain, but, on the other hand, since 
you are running into some rain, 
you might end up wetter than if 
you had walked. Try to do a rough 
calculation, taking your body as a 
rectangular object. Using such a 
model, can you tell if your answer 
(whether to run or walk) depends 
on whether the rain is falling ver- 
tically or at a slant? 


Catching a fly ball 

If in baseball a highly hit ball— a 
"high fly"— is knocked to your 
part of the outfield, there are two 
things you could do. You could 
dash over to the correct place and 
wait to catch the ball, If you do, 
I'll ask you how you guessed where 
the ball was to come down. Or, 
you might run over at a more or 

less constant speed, arriving just in 
time to make the catch. In that 
case I'll ask you how you deter- 
mined the correct running speed. 
Experience helps, of course, but 
you must also have an intuitive 
feel for the physics involved in the 
ball's flight. What tips you off as 
to where to go and how fast to 




Running a yellow light 

Every driver will occasionally have 
to make a quick decision whether 
or not to stop at a yellow light. 
His intuition about this has been 
built up by many tests and some 
mistakes, but a calculation might 
reveal some situations where 
intuition will not help. 

For some given light duration 
and intersection size, what com- 
binations of initial speed and 
distance require you to stop (or 
run a red light)? What range of 
speed and distance would allow 
you to make it through in time? 
Notice that for a certain range of 
these parameters you can choose 
either to stop or not. But there 
is also a range in which you can 
do neither in time, in which case 
you may be in a lot of trouble. 



Getting the bat there in time 

To make a hard line drive you must 
get the bat into the proper position 
for the collision with the thrown 
ball. How much error can you 
stand, both in the vertical direc- 
tion and in time, and still be able 
to get the hit? For example, 
would it be all right if your timing 
is off by some small amount such 
as 0.01 second? 


Exceptionally good reference: 
Crabtree (36). 

The walrus speaks of classical mechanics 23 


Turn or stop 

It is hard to find any physics of a 
more real-world nature than that 
which involves your own death. 
For example, suppose you suddenly 
find yourself driving toward a 
brick wall on the far side of a 
T-intersection (Figure 2.5). What 
should you do? Use your brakes 
fully, without skidding, while 
steering straight ahead? Turn at 
full speed? Or turn while applying 
your brakes as well as you can? 

Consider this question in parts. 
First, assume you can stop the car 
in time by braking and steering 
straight. Would turning instead 
also save you? Right now you 11 
probably want to think about this 
with ideal conditions. Later you 
can throw in the possibility of a 
skid, differences in road handling 

between front and rear tires, and 
brake fade. What if the straight- 
ahead option won't stop you in 
time? Should you bother turning, 
or are you doomed to an early 

If you were to find a large object 
in the road, would it be better to 
attempt a head-on stop or to try to 
steer around it? Of course, the 
answer will depend on the object's 

Don't answer quickly in any of 
these cases, for even though you 
may be very experienced, your 
intuition may be wrong. If it is 
wrong, the question becomes far 
more relevant. 


Figure 2.5 

Turn or stop for the brick wall? 


The secret of the golf swing 

How should you swing a golf 
club in order to impart maximum 
speed to the ball? While many 
golfers might prefer to keep the 
problem in the realm of the eso- 
teric, we should be able to con- 
sider it using some physics. What 
should the initial backswing angle 
be? When should you relax your 
wrists? Should the club, arms, 
and ball be along a straight line 
when contact with the ball is 

5; 6; 1613. 

momentum transfer 

center of mass motion 


Jumping beans 

Why do jumping beans jump? 
There they are, lying quietly in 
your hand, when suddenly, 
every few seconds, they jump into 
the air. Can you convince a friend 
they violate conservation of mo- 

7; 8; 9, p. 238. 



How high can you jump? Can you 
calculate the height? Would you 
be able to jump higher if your legs 
were longer? Is there any initial 

24 The flying circus off physics 

orientation or way of swinging the 
arms that would increase your 

How far can you jump? Some 
athletes bicycle their legs as they 
fly through the air; does this 
really help? At what angle is it 
best to leave the ground? At the 
angle (45°) that maximizes the 
range of a projectile? 

Why do pole vaulters and broad 
jumpers charge forward for the 
jump but high jumpers approach 
the jump much slower? Shouldn't 
all three obtain the maximum 
possible speed before they leave 
the ground? 

Can you jump as high or as far on 
a seacoast beach as you can on a 
mountain? If the height above sea 
level makes a difference, some 
caution should be exercised in com- 
paring record jumps at various 

10 through 13. 


Throwing the Babe a slow one 

Pitchers sometimes threw Babe 
Ruth slow balls because they 
thought it would be harder for 
him to hit a home run if the ball 
were moving slower when struck. 
Does this belief have any physi- 
cal basis? 

14, p. 274. 




Karate punch 

In karate classes I was taught to 
terminate a punch, kick, or edge- 
of-hand chop several centimeters 
inside my opponent's body. This 
is different from normal street 
fighting where there is much 
follow through. Which technique 
will produce more damage? 
Through a rough calculation, can 
you show the feasibility of a karate 
fighter breaking a wooden board, 
a brick, or a human bone with a 




Should a sculptor use a heavy 
hammer or a light one on his 
chisel? Which hammer should be 
used to drive a nail? When would 
an elastic collision (that is, one 
with a full rebound of the hammer) 
be more desirable than an inelastic 
collision? Consider something on 
a grander scale, a piledriver, for 
example: should the piledriver be 
heavy or light compared to the 
pile? A guess is easy to make, but 
a calculation should back it up. 

15; 16, pp. 396-399. 



Softballs and hardballs 

Should you hit a hardball and a 
Softball differently? In particular, 
should there be more follow 
through for one than for the other? 


Heavy bats 

Why do home-run hitters prefer 
heavy bats? It seems it would 
be harder to give the heavy bat a 
large final speed and hence harder 
to hit the ball very far. Should you 
use the heavy bat for a bunt? Con- 
sidering the range of weight normal- 
ly used, does the bat's weight 
really make much difference? 


center of mass motion 


Jerking chair 

A body's center of mass moves 
only if an external force is applied, 
but you can get to the other side 
of the room in a chair without 
letting your feet touch the floor. 
If all your twistings and contor- 
tions are internal forces, what 
provides the external force? 

The walrus speaks off classical mechanics 25 



pressu re 



Click beetle's somersault 

If you poke a click beetle lying on 
its back, it throws itself into the 
air, as high as 25 cm, with a notice- 
able click. That in itself is trifling, 
you say? But the beetle, without 
using his legs, hurls himself up- 
ward with an initial acceleration 
of 400 g and then rotates his body 
to land on his legs. 400 g! Even 

more surprising is that the power 
needed for this is 100 times the 
direct power output of any 
muscle. How does the beetle 
produce such an enormous power 
output? How frequently can he 
perform this amazing feat, and 
what physically determines the 

21; 1485; 1531. 


momentum transfer 



Balanced hourglasses. 
Sand in bottom of each. 

Figure 2.16 

The weight of an hourglass. 


The weight of time 

Does the weight of an hourglass 
depend on whether the sand is 
flowing (Figure 2.16)? If some 
of the sand is in free fall, won't 

If you tip over an hourglass, 
does it weigh less? 

the weight of the hourglass be 



Pressure regulator 

Have you ever used a pressure 
cooker? Mine has a solid cylinder 
on top of the lid that somehow 
regulates the pressure. There are 
three different size holes drilled 
into the side of the cylinder, and I 
pick the pressure by placing the ap- 
propriate hole over the hollow stem 
extending from the pan (Figure 
2.17). How does it work? The 
pan's steam must lift the same 
cylinder no matter which hole I 
pick. Why do I get different pres- 
sures by using different holes? 

Figure 2.17 
Pressure regulator. 

26 The flying circus off physics 



The superball as a deadly weapon 

If a small superball,* which is a 
very elastic rubber ball, is dropped 
immediately after a large one as 
shown in Figure 2.18a, the small 
ball will be sliot back up into the 
air after the two balls strike the 
floor. If the mass of the small 
ball is appropriately chosen, the 
other ball will completely stop at 
the floor and the smaller ball will 
rebound to about nine times its 
original height. 

Try this as well: drop a large 
superball, a small superball, and a 
ping-pong ball as shown in Figure 
2.186. If the balls are appropriate- 
ly chosen, the ping-pong may 
reach almost 50 times its original 

18 through 20. 

*® Wham-0 Manufacturing Company, 
San Gabriel, California; similar balls are 
sold under other brand names. 



Smaller ball 
shot upward. 

Larger ball 


Ping-pong ball. 
Two superballs. 

Figure 2.18 

Rebounds of several superballs 

dropped simultaneously. 


2.19 through 2.22 


Locking brakes 

If you must stop your car in a 
hurry, should you slam on the 
brakes and lock them? 


Wide slicks on cars 

If you had to decide between 
regular-width tires with no treads 
and wide tires with no treads (both 
are called slicks), which would you 
choose for better braking ability? 

In drag racing wide slicks are 
preferred for the rear tires. Why? 




Friction in drag racing 

In drag races there are two mea- 
surements of interest: the final 
speed and the total elapsed time 
on a quarter-mile course. To 
help gain traction, a sticky fluid 
is poured under the rear wheels 
before the "go" light, but ap- 
parently the track's friction really 
affects only the elapsed time and 
has little influence on the final 
speed. Why? 


The walrus speaks of classical mechanics 27 

I ' I ' I ' 1 

\J.— ►■ ' «— u 

Figure 2.22 

Sliding your index fingers under a yardstick 


Sliding stick across fingers 

Hold a yardstick horizontally on first on one finger and then on the 

your index fingers and slide your other, and so on. Why does the 

fingers together smoothly (Figure sliding change back and forth? 

2.22). Does the stick slide smoothly 00 _ . 00 OA 
*• o xt -4. i-j 23; 24, pp. 83-84. 

over your fingers? No, it slides 

Rational kinematics 
and dynamics 

2.23 through 2.55 

angular motion 

angular momentum 


rotational Bnergy 

moment of inertia 


Accelerating and braking in a turn 

Why is it unwise for you to do any 
significant braking when your car 
is in a turn? For example, suppose 
that while in the curve you decide 
you are taking it a bit too fast. 
What happens if you apply the 
brakes too hard? 

Race drivers accelerate as they 
are leaving a curve, not while 
they are in it. Why? 

29; 30, p. 8. 




Starting a car 

There is much debate about how to 
start a stick-shift car on a slippery 
road. Some claim you should have 
the car in low gear; others swear 
you must put it in high. Why does 
the gear you use matter at all? 
What is needed to get the car mov- 
ing? Why must the initial speed be 
small? What advantages would 
any one gear have over the others? 
You'll have to explain how the 
torque applied to the wheel de- 
pends on the gear and decide 
when you need more or less torque. 


angular and linear 
momentum conservation 



Left on the ice 

For a mean trick, your friends 
desert you in the middle of a 
large frozen pond. The ice is so 
very slippery that you can't walk 
off in a big huff, or even crawl off 
in a small one. How can you get 
off the ice? 

Now let us suppose you were 
first placed on your back. After 
lying there for a while, your back 
is frozen to the bone and you want 
to turn over. How do you do it on 
such slippery ice? 

They could have been meaner. 
They could have stood you up and 
tied you to a pole fixed in the ice 
(Figure 2.25). How could you turn 
yourself about that pole if they 

Figure 2.25 

28 The flying circus of physics 

had left your hands free? The pole 
is too slippery to use, and the ice 
is too slick to turn with your feet. 
How then do you turn around to 
face the other way? 

9, p. 238. 


center of gravity 


Turning a car, bike, and train 

How do you turn a bicycle? How, 
exactly, do you initiate the turn? 
On a motorcycle you turn by 
leaning the bike and not by turn- 
ing the handle bars. Why the dif- 

When a train goes around a curve 
it leans because the roadbed is 
banked to prevent the centrifugal 
force from derailing the train. Will 
the leaning also affect the turning 
as in the motorcycle case? Try a 
rough, back-of-the-envelope cal- 
culation to see. Whether or not 
the effect is significant or even real, 
the outside rail on a curve is often 

Finally, do you have a similar 
consideration in turning high speed 
cars, such as the Formula 1 race 

16, pp. 535-536; 24, pp. 156- 
157; 35; 36, pp. 43-44; 37, pp. 
146-147; 38, pp. 89-93; 1612. 


linear kinematics 


Pool shots 

How do you set up a "follow shot" 
(the cue ball follows after the ball 
with which it has collided) or a 
"draw shot" (cue ball returns after 
the collision). I thought that if a 
moving object hits a stationary ob- 
ject of the same mass, the first 
object stops. 

A masse shot is one in which the 
cue ball describes a parabolic path 
(Figure 2.27a). (These shots are 
usually outlawed in most pool 
halls for a missed masse shot will 
rip up the table cover.) How 
must the cue ball be hit to bring 
this about and why, in detail, does 
it happen? 

Why is the cushion higher than 
the center of the balls (Figure 
2.27b)? Wouldn't you get better 
rebounds if the cushion were at 
the center's height? 

How can English be used in a 
cushion shot? 

14, pp. 143-146; 24, pp. 158- 
161, 250-251; 25; 26, pp. 183- 
186; 27, pp. 139- 143, 268-274, 

Figure 2.27a 
Masse shot. 


Figure 2.27b 
Height of cushion. 

The walrus speaks off classical mechanics 29 


Figure 2.28 

Superball tricks (after drawings copyrighted 1970 by Wham-O Manufacturing Co., used with permission). 


Superball tricks 

One of the most significant 
advances made by our technolog- 
ical society is the Superball*. 
Because of its high elasticity it can 
perform some rather amazing tricks. 
Several are shown in Figure 2.28. 

Figure out how you set up each 
trick and explain how they work. 

31; 32. 

*® Wham-O Manufacturing Company, 
San Gabriel, California; similar balls are 
sold under other brand names. 


mechanical efficiency 


Bike design 

Why is a modern bicycle designed 
the way it is? In the past there 
has been a great variety of designs 
(Figure 2.29a). Some, for 
example, had radically different 
wheel sizes, and some had the 
pedals attached to the front wheel. 
Is the modern bike more efficient 
or more stable than its predeces- 

Why does the modern bike have 
a curved front wheel fork? Would 
the bike be more or less stable 
with the other possible fork de- 

signs shown in Figure 2.29b? 

35; 39; 41; 42, Vol. II, Chapter 
6; 43. 

Figure 2.29b 

Figure 2.29a 

30 The flying circus of physics 

resonant driving force 



The Hula-Hoop* is a plastic hoop 
that can be kept rotating about 
your waist by an appropriate cir- 
cular motion of your hips (Figure 
2.30). The toy was first popular 
in the 1950s, but similar hoops 
rotated about the arm or leg have 
been used for toys and in dances 
for a long time. The American 
Indians, for example, used them 
in some types of hoop dances. 
Think about what it takes to 
keep a Hula-Hoop up and going. 
You throw it around your waist 
and then trap it with your driving 
hula motion. Should the initial 
speed you give it be more than the 
speed at which you are going to 
trap it? How do you drive it 
around? Is the hoop's motion in 
phase with yours? What is the 
minimum speed you can use? 


Figure 2.30 

*® Wham-O Manufacturing Company, 
San Gabriel, California. 

Figure 2.31 

"Nobody likes to fall, Rocco—but 
this is ruining our image. " The 
Saturday Evening Post 




Keeping a bike upright 

How do you keep your balance on 
a bicycle? When you sense a fall, 
do you steer into the fall and there- 
by right the bike? Or does the 
bike itself do most of the stabiliz- 
ing? It must at least contribute 
some stability because if it is 
pushed off riderless it will stay up 
for almost 20 seconds. 

How do you balance and steer 
the bike when you ride without 
using your hands? Suppose you 
stand next to the bike and you 
lean the bike to the right. Which 
way does the front wheel turn and 

24, pp. 156- 157; 35; 36, pp. 43- 
44; 37, pp. 146- 147; 38, pp. 89- 
93; 42, Vol. II, Chapter 6; 43; 44, 
pp. 122-123. 

driven rotational motion 


Cowboy rope tricks 

How does a cowboy keep his lasso 
up and spinning? What minimum 
speed must he maintain in order to 
keep the lasso horizontal? Vertical? 

33; 120. 

moment of inertia 



Spinning a book 

If you hold it closed with a rubber 
band, you can toss this book into 
the air spinning about any of the 
three axes shown in Figure 2.33. 
The motion about two of the axes 
is a simple, stable rotation. The 
rotation about the third axis, 
however, is much more complicated, 
no matter how carefully you throw 
the book. (See Figure 2.33.) Try 
it. What causes that uncontrollable 
wobbling about the third axis? 

44, p. 115. 

Figure 2.33 

The walrus speaks off classical mechanics 3 1 

energy conservation 




Fiddlesticks* is a remarkably simple 
yet fascinating toy. It consists of a 
plastic ring (of relatively large inner 
diameter) on a stick. Once the 
ring is sent spinning by a flick of 
your fingers, the stick is held ver- 
tically. The ring begins to drop 
(slower than you would expect), 
and as it comes down the stick, 
the ring spins faster and falls 
even slower (Figure 2.34). By in- 
verting the stick just before the 
ring reaches the lower end of the 
stick, the process can be repeated 
indefinitely. Why does the spin 



Figure 2.34 

increase as the ring falls? In fact, 
why doesn't the ring just fall 
with the full gravitational ac- 

Now use two rings at once. Not 
only is this more spectacular, but 
a curious thing often happens. 
The top ring may be dropping 
faster than the lower ring and thus 
may run into the lower ring. If 
this occurs, the rings bounce 
apart, the upper ring rising (Figure 
2.34). Why? 

*® Funfair Products, Inc., New York, 
N.Y. 10016. 

moment of inertia 



center of gravity 


Eskimo roll 

How does a kayaker right an 
overturned kayak without ever 
leaving the cockpit? 

45; 1563. 


Large diameter tires 

Will large diameter tires really 
make your car go faster? 


Car in icy skid 

If your car starts to skid on an 
icy road, are you supposed to 
straighten it out by turning the 
front wheels in the direction in 
which you want to move or in the 
direction of the skid? Why? 



Tire balancing 

If your tire is balanced statically 
with a simple bubble leveler, will 
it still be balanced when it's 
spinning? Can you get both static 
and dynamic balancing with a 
single balancing weight added to 
the rim? How about two? 



moment of inertia 


Tearing toilet paper 

Why, on some toilet paper dispens- 
ers, can I get a long piece of toilet 
paper without tearing if the roll is 
fat, but when the roll has been 
nearly used up, the paper inevita- 
bly breaks too soon, giving only 
short pieces? Why is just the op- 
posite true for other dispensers? 

32 The flying circus off physics 


angular momentum 


Skipping rocks 

How does a stone skip across the 

being fired upon. So, the RAF 

against the wall and made it 

water? If you skip a stone across 

developed a bomb (cylindrical, 

crawl downwards until it 

hard-packed, wet sand, the marks 

with a length of about 5 feet and 

exploded, on a hydro- 

in the sand provide a record of the 

a slightly smaller diameter) which 

static fuse set for 30 feet 

stone's flight. You'll find the 

was given a backspin around its 

below surface, still clinging 

first bounce is short (several inches), 

length of about 500 rpm in the 

to the dam. It was a beauti- 

the next is long (several feet), and 

plane's bomb bay before it was 

fully simple idea for position- 

this sequence repeats itself over and 

released over the target (Figure 

ing a bomb weighing almost 

over until the stone comes to rest 


10,000 lbs to within a few 

(Figure 2.40a). Why does it follow 

When it hit the water, the 

feet. * 

this pattern? 

bomb skimmed like a stone, 

48; 49; 1486. 

During World War II the skipping 

bouncing in shorter and 

rock effect was used by the British 

shorter jumps until it hit 

in the bombing of German dams. 

the dam itself. Then, in- 

*From The Royal Air Force in World 

War II , edited by Gavin Lyall, copyright 

It is very difficult to drop a bomb 

stead of rebounding away, 

© 1968 by Gavin Lyall. Published by 

on a dam, especially when you are 

the back-spin forced it 

William Morrow and Company, Inc. 

Figure 2.40a 

Path of skipping rock on sand. 


| ^~ 

^—- <W I I I ITTTT^ / 





"" *" *- rj 

Figure 2.40b 

The skipping-rock bomb. 

«--^ „--- < ~- 

^ : ^Kv^ 

The walrus speaks of classical mechanics 33 




angular momentum 


angular momentum conservation 


Car differential 

angular momentum 


Falling cat 


Carnival bottle swing 

When your car takes a turn, the 
outside wheels must move faster 

There's an old carnival sideshow 
trick involving hitting a bottle 

It is common knowledge that if 
you drop a cat upside down it will 
land on its feet; even tailless cats 

than the inside wheels. Since 
there is an inside and an outside 
wheel on each axle, how is this 
turning accomplished? 

with a pendulum suspended 
directly above it (Figure 2.44). 
To show your skill, you must 
start the pendulum so that it 

show this mysterious ability to 
right themselves. Now, if there is 
no external torque the cat's angular 
momentum must be constant. Is 

24, PP. 254-255; 52, pp. 500-501. 

misses the bottle on the forward 
swing and then hits it on the 
return swing. The barker, of 
course, won't let you throw the 
pendulum over the top. Still, 
this trick shouldn't be too hard, 
should it? With a few tries you 
should find the arc needed to win 
the prize. Well, try it, and then 
worry about why it doesn't work 
and then about what would make 

the angular momentum constant 
during the fall? If so, how does 
the cat turn itself through a full 
180°? If the angular momentum 
is not conserved then somewhere, 
somehow, there must be a torque 
on the cat. But where? References 
36 and 54 contain photographs 
of a cat turning over, and they are 
clear enough to provide an explana- 

moment of inertia 


Racing car engine mount 

Some of the European racing cars 
have their engines mounted in the 

centers of the cars, rather than in 
the fronts or rears. The racing 

it work. 
53, p. 184. 

9, p. 238; 36, pp. 56-57; 54; 

circuits in Europe are really just 

streets and therefore have lots 

of fast turns. Considering the 


torque needed to turn a car, 


Ski turns 

what advantages does a 


center-mounted engine have 


A ski turn can be a set of rather 

over the conventionally mounted 

\ -'"". 

complicated twists and gyrations 

engine in this situation? 

but consider the several simple 

^ V ' 

elements of such a turn. 

The Austrian turn requires a 
sinking of the whole body, followed 

center of gravity 



1 * 

by a powerful upward thrust and a 


rotation of the upper part of the 


.- -^ 

body. The lower part, and hence 

Tightrope walk 

.- s. 


the skis, rotate the opposite way 
as a result. Why? For a given 

How does a tightrope walker keep 

Figure 2.44 

upper-body rotation, how much 

his balance? Why does a long bar 

Swing the ball so as to hit the 

does the lower body turn? 


bottle on the return swing. 

34 The flying circus of physics 

The normal skiing stance gives a 
straight skiing path, but a shift of 
one's body either forward or back- 
ward on the skis will force a turn. 
Why and which direction of 
shifting gives which sense of turn? 

If the skis are edged (the ski's 
uphill edge is held into the snow so 
that the ski is at an angle to the 
snow's surface), turns are also 
caused by a shifting of weight, but 
the sense of turn is opposite to 
that in the normal-stance case. 
Why is that, and again, what forces 
the turn? 

55; 1525. 



Can you tell me why a yo-yo comes 
back up? How about the sleeping 
yo-yo in which the yo-yo is thrown 
down and spins at the end of the 
string until it returns when you 
give the string a slight jerk. If the 
sleeping yo-yo touches the floor, 
it will walk along the floor- this is 
"walking the dog." 

As an even better trick, put the 
yo-yo to sleep, take the string off 
your finger and hold it between 
your thumb and index finger. Now 
give that hand a slap. As soon as 
the yo-yo starts to climb back up, 
let go of the string. The yo-yo 
will charge up the loose string, 
neatly winding it up. Dazzle your 
friends by catching the yo-yo in 
your coat pocket when the string 
is wound up. 

24, pp. 246-247; 56. 


Slapping the mat in judo 

When you've been thrown in judo, 
slapping the floor with your arm 
at the moment of impact will pre- 
vent injury in the fall. How does 
it work? The effect is probably 
partly psychological, but I know 
that for the most part it is real. 
When I was taking lessons, I was 
always hurt when I missed the 
slap or when my timing was off. 
When I slapped the mat properly, 
my discomfort was only mild. 

angular momentum 




Bullet spin and drift 

Why are bullets given a spin as 
they travel down the rifle barrel? 
The rifle, in fact, derives its name 
from the rifling-the spiral grooves 
in the bore -that impart this spin. 
If the bullet is given a counter- 
clockwise spin as seen from the 
rear, it will drift to the left of the 
target. A clockwise spin will cause 
a drift to the right. Why? Can you 
calculate, roughly, the amount of 
drift for small and large guns? 

16, pp. 536-537; 26, pp. 154- 
155; 36, pp. 53, 140- 144; 37, 

pp. 148 ff, 274 ff; 38, pp. 1 17- 
1 19; 40, pp. 440-44 1; 64, pp. 


Figure 2.50 

Leaving a leaning tower for a 



The leaning tower of books 

If you want to construct a stack of 
books leaning to the side as much 
as possible (Figure 2.50 ), what is 
the best way to stack them? 
Would you put the edge of one 
book over the center of the lower 

57 through 59; 1559. 

The walrus speaks of classical mechanics 35 


angular momentum 

center of gravity 

stress and strain 


Falling chimneys 

When a tall chimney falls, it 
usually breaks in two at some point 
along its length. Why doesn't it 
fall in one piece? Where do you 
think the break will occur? Will 
the chimney bend towards or away 
from the ground after the break 
(Figure 2.51a)? You can check 
your answer by toppling a tall stack 
of children's blocks and seeing 

which way the stack curves as it 

If the chimney does not break, 
something even stranger may occur: 
the base of the chimney may hop 
into the air during the fall (Figure 
2.515). How can it do this, 
seemingly against gravity? 

9, pp. 124- 125; 60 through 63. 

(a) Which way will a chimney break? 
Figure 2.51 

(b) If it doesn't break, it may hop up. 

forces in a rotating frame 

forces in a rotating frame 


The Falkland Islands battle and Big 

During World War I, there was a 
famous British-German naval fight 
near Falkland Islands (about 50°S 
latitude) in which the British shots, 
while well aimed, were mysteriously 
landing about a hundred yards to 
the lefrof the German ships. The 

British gun sights were not faulty, 
for they had been set very precisely 
back in England. During the 
German shelling of Paris in the 
same war, a huge artillery piece 
called Big Bertha would pump 
shells into the city from 70 miles 
away. If normal aiming procedure 
has been employed, Big Bertha's 
shots would have missed their 
mark by almost a mile. What was 
happening to the shells? 

68 through 72; 1488. 


Beer's law of river erosion 

Why does the right bank of a river 
in the northern hemisphere suffer 
more erosion, on the average, than 
the left bank? 

24 f p. 164; 72; 73. 


A new twist on the twirling ice 

The twirling ice skater has long 
been used as an example of the 
conservation of angular momentum 
When she pulls her arms in, she 
spins faster due to the conserva- 
tion of angular momentum (there 
are no external torques). 

This is all true, of course, but I 
would like to explain the speeding 
up in terms of forces because 
force arguments are more acces- 
sible to the imagination than 
angular momentum arguments. 
What is the force that speeds up 
her spinning? 


36 The flying circus of physics 

airfoil theory 

angular motion 



Returning boomerangs are designed 
to be thrown great distances and to 
return to the thrower. Australian 
natives have thrown them as far as 
100 yards and to heights of 150 
feet with five complete circles. 
The nonreturning type, which is 
more practical for hunting, can be 
thrown as far as 180 yards. 

The ordinary boomerang is 
shaped like a bent banana. Is 
it essential that the boomerang 
have this particular shape? Can one 
make a returning boomerang in 
the shape of an X or a Y? Most 

boomerangs are designed to be 
thrown with the right hand. What 
is the difference between left- 
and right-handed boomerangs? 
Why does a boomerang (of any 
shape) return? Why does it loop 
around in its path (see Figure 
2.55)? Finally, how does the 
path depend on the boomerang's 
orientation as it leaves the 
thrower's hand? 

26, pp. 153- 154; 37, pp. 29 1- 
296; 65 through 67; 1564. 


Figure 2.55 
Boomerang path. 

Periodic motion 

(2.56 through 2.68) 

angular momentum 


potential and kinetic energy 

center of gravity 



When you swing, you must pump 
first to gain height and then just 
to keep going. How does pump- 
ing work? How do you pump if 
you want to start to swing from 
rest? Do you pump differently 
when you are sitting and standing? 
Is it possible to turn a complete 
circle on a well-oiled swing, or is 
there some limit to the height you 
can reach? You might want to 
consider a swing hung on rigid 
bars as well as on chain or rope. 
How much work do you do in 
pumping from rest to some maxi- 
mum height? 

9, p. 239; 26, pp. 245-246; 42, 
Vol. I, pp. 179-181; 75 
through 80. 




Soldiers marching across footbridge 

In 1831 cavalry troops were travers- 
ing a suspension bridge near 
Manchester, England, by marching 
in time to the bridge's swing. The 
bridge collapsed. Ever since then, 

The walrus speaks of classical mechanics 37 

troops have been ordered to break 
step when crossing such bridges. 
What is the common explanation 
for the danger, and is the danger 
real? Make rough calculations if 
you can. 

81, pp. 59-60; 82, pp. 193- 194; 

resonant oscillations 


Road corrugation 

A road that is initially flat may 
develop a bump, and soon there- 
after ripples appear down the 
road. In fact, the ripple itself 
seems to propagate slowly along 
the pavement. Thus many un- 
paved roads and even some black- 
tops and concrete roads look like 
washboards, especially after a 

rain leaves the depressions filled 
with water. 

A similar pattern has been ob- 
served on trolley car and railroad 
tracks. A train passing over such 
corrugation makes so much noise 
that the tracks are called "roaring 
rails." Skiers may also find a wash- 
board surface on their ski trails. 
What causes such corrugation? 
What determines its periodicity? 
Can you predict the periodicity 
by simulating the effect in a sand- 
box with a hand-held wheel? 


torques, angular momentum 

energy change, resonant oscillations 


Incense swing* 

Pilgrims to Santiago de Campostella, 
Spain, visit the shrine of St. James 
to burn incense. The incense and 
charcoal are held in a large silver 
brazier hung from the ceiling. 
The brazier is set swinging with a 
small amplitude, and then it is 

pumped by about six men (see 
Figure 2.58) until it is swinging 
through 180°. The swinging makes 
the charcoal burn energetically for 
the pilgrims. The pumping is the 
interesting part: they do it by 
shortening the rope by about a 

meter each time it passes through 
the vertical; they release the same 
amount of rope when the container 
reaches its maximum height. How 
does this shortening and lengthening 
of the rope increase the amplitude? 
*H. Pomerance, personal communication 

Figure 2.58 

38 The flying circus of physics 

coupled harmonic motion 

pendulum motion 

coupled harmonic motion 



A ship's antiroll tank 

A ship's rolling is normally just 
unsettling, but if the waves strike 
the ship at its resonant frequency, 
the rolling can be very dangerous. 
Consequently, some ships have 
carried tanks partially filled with 
water to diminish the danger 
(Figure 2.60). Such a tank had 
carefully chosen dimensions so 
that the resonant frequency of 
the water it held matched that of 
the ship. But isn't there some- 
thing wrong? Since the resonant 
conditions were matched, how 
could the tank have managed to 
stop the resonant buildup of 
the ship's rolling? 

44, p. 270; 88, pp. 202-203. 














^I 1 : 1 ! 1 ! 1 ! 1 ! 1 ! 1 : 

I 1 ! 1 ! 1 ! 1 ! 1 ! 1 ! 1 ! 1 ! 1 ^ 

Figure 2. 60 

The antiroll water tank in a ship, 

as shown in cross section. 

Figure 2.61 

If the plate is oscillated vertically 
fast enough, the pendulm won't 
fall over. 


Inverted pendulum, unicycle riders 

Suppose you inverted a pendulum 
and tried to stand it on its end. It 
would be unstable and would fall 
over at the slightest disturbance. 
But if the pendulum were made 
to oscillate up and down fast 
enough (Figure 2.61), it would be 
stable even against small distur- 
bances. A unicycle rider accom- 
plishes the same thing, except that 
he uses a horizontal oscillation to 
stabilize himself. Why is there 
more stability in the oscillating 
cases? What determines the 
oscillation frequencies needed to 
gain such stability? Rather than 
use equations entirely, can you 
explain the inverted pendulum 

83 through 87; 795. 


Spring pendulum 
You are already familiar with 
springs and pendulums, but have 
you considered putting them 
together by suspending the pen- 
dulum bob on a spring? If you 
choose the spring and the bob 
appropriately you will have a 
remarkable example of sym- 
pathetic oscillation. Just as 
you would expect, a vertical 
pull sets up vertical oscillations; 
but soon the vertical motion 
dies away, and the bob begins 
to swing like a pendulum (Figure 
2.62). After a short time it is 
again oscillating vertically. Some- 
how the energy of the system 
moves back and forth between 
the two oscillatory modes and 
continues to do so as long as there 
is energy left in the system. How 
must you choose the bob's mass 
and the spring's mass and length 
to obtain this oscillation exchange? 
Why does the exchange take place 
at all? With what beat frequency 
does the bob switch from mode to 

Figure 2. 62 

The walrus speaks of classical mechanics 39 

coupled pendulum motion 


The bell that wouldn't ring 

There's no sense in putting up a 
bell refusing to ring, but that's what 
was done at the Cathedral of 
Cologne. The pendulum frequencies 
of the bell and its clapper were so 
unfortunately chosen that the bell 
and clapper swung in phase, and of 
course the bell won't ring that way. 
Under what conditions will the 
pendulum motions be so matched? 
And when it does happen, what 
can you do about it, short of 
throwing the bell out of the belfry? 

16, pp. 409-4 13; 37, p. 148. 

Figure 2.63 

"It dings when it should dong. " 

coupled harmonic motion 


Swinging watches 

Once hung on a chain, free to 
swing, should a pocket watch 
change its timekeeping rate? 
Many pocket watches do, even 

though they keep very good time 
if fastened down securely. If hung 
free on a chain by its stem (Figure 
2.64), the watch will gradually 
begin to swing and may gain or 
lose up to 10 or 15 minutes a day. 
Why does it swing, and why does 
the timekeeping get messed up? 
Finally, why do some watches gain 
time while others lose time? 

16, pp. 420-424; 24, pp. 1 14- 
11 7; 42, Vol. II, pp. 85-87, 
190; 90. 

Figure 2.64 

Swinging pocket watch. 



standing waves 


Earth vibrations near waterfalls 

Waterfalls pound the earth so hard 
that you can feel the vibration in 
the ground from a considerable 
distance. For most waterfalls one 
frequency of vibration is dominant, 
and the frequency is higher, the 


shorter the waterfall. In fact, the 
product of the frequency and the 
height of the waterfall is always 
one fourth the speed of sound in 
water. Why should the frequency 
have anything to do with the water- 
fall's height, and why in the world 
should their product be one-fourth 
the speed of sound? 



vibrational modes 


Stinging hands from hitting the ball 

Sometimes when you're batting a 
ball, your hands may get a good, 
healthy sting. The sting is related 
to what part of the bat hits the 
ball. Not only can such a collision 
cause a sting, but also it makes it 
much more likely the bat will break. 
Why are there such points on the 
bat, and where are they? 



The archer's paradox 

No matter how well an arrow is 
aimed, when it is loosed and the 
feathered end is passing the bow 
grip, it will deviate considerably 
from the line to the target, perhaps 
as much as 7° (Figure 2.67). The 
archer's paradox is that a well- 
aimed arrow will still strike the 

40 The flying circus of physics 

Top view 

Figure 2.67 

Once the arrow is loosed, it 

doesn't point toward the target. 

target. How can this be? First 
of all, why is there a deviation 
and second, given the fact of the 
deviation, why does the arrow 
then hit the target? 

High-speed photographs of the 
arrow show that the last time 
the arrow touches the bow's stock 
is when it is first loosed. It 
does not touch the stock even as 
the feathered end passes. If that's 
true, how does the arrow find its 
way to the target? 



driven rotation phase 


Magic windmill 

A fascinating toy which you can 
easily build yourself is the rotor 
on a notched stick (Figure 2.68a). 
One stick has notches along its 
length and a small propeller on the 
end (on a straight pin jammed into 
the stick). The second stick is 
used to stroke the notches. Hold- 
ing your forefinger on the far side 
of the notched stick and your 
thumb on the near side, run the 
stroking the stick back and forth 
notches, as shown. As you are 
stroking, let your forefinger press 
against the notched stick (Figure 
2.68a). The propeller will turn 
in one direction. Now loosen 
your forefinger and let your 
thumb press against the stick, 
stroking the stick back and forth 
all the while. The propeller will 
turn in the opposite direction. 
When you're showing this to 
the uninitiated, you can slyly 
shift from the forefinger to the 
thumb and make a great mystery 
of the change of direction of the 

(a) Single rotor 



Figure 2.68 

Magic windmill (After R. W. Leonard, Am. J. Phys., 5, 175 (1937). 

spin. The number of lies you can 
feed someone about why the rotor 
reverses is almost unlimited— I like 
to attribute it to a variation in 
cosmic ray intensity. 

The first question you should ask 
yourself is why the rotor turns at 
all. Next comes the bigger mystery 
of why the spin sense depends on 
which side of the stick you press. 

If you want something flashier, 
put four rotors on the stick (Figure 
2.68 b). All four will turn in the 
same direction, so there's nothing 
essentially different about this. 
Another design, which is more dif- 
ficult to explain, has two rotors 
mounted one behind the other 
(Figure 2.68c). Something strange 
does happen in this case. You can 
make both rotors turn to the left 
or both to the right or, best of all, 
you can make one go in one direc- 
tion and the other in the opposite 

93 through 96; 1487. 
(b) Four rotors (c) Opposing rotation 


The walrlis speaks of classical mechanics 4 1 

Gyroscopic motion 

(2.69 through 2.73) 



angular momentum 


Personalities of tops 

Why does a spinning top stay up? 
Can you explain it using only 
force arguments, without invoking 
torque and angular momentum? 
The top stays up against gravity; 
hence, there must be a vertical 
force. What produces that force? 

Can you also explain the personal- 
ities of individual tops? Some 
"sleep/' that is, remain vertical; 
others precess (Figure 2.69) like 
mad. Some are always steady in 
their motion; others are worri- 
some before finally settling down 
to a steady motion. Some die long, 
lingering deaths; others depart 
rapidly. How do you account for 
these varied temperaments? 

36; 37, Chapter 1. 


Figure 2.69 

In precessing, the top's axis 

itself rotates about the vertical. 

Figure 2. 70 



The diabolo, an ancient toy, is a 
spool made of two cones stuck 
together, which is spun by means 
of a string whose ends are tied to 
sticks (Figure 2.70). Spinning is 
initiated by first lowering the right 
hand, smoothly drawing it back 
up and thus spinning the diabolo, 
then quickly dropping that hand 
again and repeating the process 
until sufficient spin has been 
given the diabolo. 

Why is the diabolo so much 
more stable when spinning? Even 
then, you may have to make cor- 
rections. For instance, suppose 
the near end begins to dip. What 
should be done with the sticks to 
make the spool horizontal again? 
Or suppose that you want the 
spool to turn to your left. What 
must you do with the sticks? 

36, pp. 40-41, 120-121; 

37, pp. 458-459. 


Spinning eggs 

In times of doubt, you can 
distinguish a hard-boiled egg from 
a raw one by spinning them. The 
cooked egg will stand on end and 
the raw one will not. Why? 
Another way to tell if an egg is raw 
or cooked is to spin it, stop it with 
your finger, and quickly release it 
(Figure 2.71 ). A cooked egg will 
sit still, but a raw one will begin 
to turn again. Again, why? 

36, pp. 5-6, 51, 155;, 37, pp. 
16-17,264-272; 108; 109, 
pp. 39,57; 110, p. 123. 

Figure 2. 71 

Testing for a fresh egg. 


The rebellious celts 

Some of the stone instruments 
made by primitive men in England 
display curious personalities when 
they are spun on a table. These 
stones, called celts, are generally 
ellipsoidal in shape. When you 
spin them about the vertical axis 
some behave as you would guess, 
but others act normally only 
when spun in one direction about 
the vertical (Figure 2.72a). If you 
spin them in the other sense, the 

42 The flying circus of physics 

Figure 2. 72a. 
Spinning celt. 

rebellious stones will slow to a 
stop, rock for a few seconds, and 
then spin in their preferred direc- 
tion. Some stones demand one 
direction, others demand the op- 

If you tap one of these stones 
on an end, say at point A in 
Figure 2.72 b, it will rock for a 
while. But soon the rocking 
ceases, and the stone begins to 
rotate about the vertical axis. 

Try to make some wooden celts 
displaying this rebellious nature. 
What causes such personalities? 

26, pp. 204-205; 36, pp. 7, 
54; 37, pp. 363-366. 

Figure 2.72b. 

Celt initially set rocking at 

A begins to spin. 


Tippy tops 

There is a kind of top that really 
knocks me out-it is part of a 
sphere with a stem in place of the 
missing section (Figure 2. 73). 
Given a spin on its spherical 
side, it will quickly turn over and 
spin on the stem, the heavier side 
thus rising against gravity. Why 
does it rise? What forces the top 
up? Isn't it completely contrary 
to your intuition that the spin- 
ning top is so unstable in the ini- 

Initial orientation 

tial orientation and so much stabler 
in the final one? 

The same behavior can be seen 
with high school and college rings 
having a smooth stone. Foot- 
balls and hard-boiled eggs will 
also raise themselves up on their 
points when spun in similar 

36, pp. 5-6,51, 155; 97 
through 108; 109, pp. 39-57. 

Final orientation 

Top turns upside down 

Figure 2. 73 


(2.74 through 2.79) 


kinetic and 





moment of inertia 


Seeing only one side of moon 

Why do we see only one side of 
the moon? Because the moon 
turns on its own axis at such a 
rate that as it orbits the earth it 
always presents the same face to 
us. But is this pure chance? 

26, pp. 369 ff; 1 1 1. 


Spy satellites over Moscow 

The United States would like to see 
what Russia is up to, so we put up 
spy satellites with long-range 
cameras. We would really like to 
have a permanent satellite stay 
directly over Moscow 24 hours 
a day. Why don't we? Why, in- 
stead, do we put up a series of 
satellites whose times over Moscow 

The walrus speaks of classical mechanics 43 


Moon trip figure 8 

When the astronauts go to the 
moon, why is their path (earth- 
moon-earth) essentially a figure 

8 (Figure 2.76) instead of an el- 
lipse? In particular, does the 
figure-8 path require less energy? 

Figure 2. 76 


Earth and sun pull on moon 

How large do you think the sun's 
pull on the moon is, compared to 
the earth's pull? Well, after all, 
the sun doesn't steal our moon 
away, so the earth must be 
pulling harder, right? That's 
satisfying, but unfortunately it 
isn't true. The sun pulls more 
than twice as hard as the earth. 
So why don't we lose the moon? 



Making a map of India 

I have read it is difficult to survey 
India because the plumb line one 
uses in surveying is pulled north- 
ward to the Himalayas and thus 
does not hang toward the earth's 
center. Is this true? How large do 
you think the effect is, and is it 
large enough to influence large- 
scale surveying? 

13; 1 18; 1 19. 


Air drag speeds up satellite 

Artificial satellites don't orbit the 
earth forever. Eventually the 
earth's atmosphere, thin as it may 
be up there, will bring them down. 
But did you know the linear speed 
of a satellite in a nearly circular 
orbit will increase because of the 
air drag? The satellite will experi- 
ence an acceleration forward along 
its path, and the accelerations^ mag- 
nitude will be the same as if the air 
drag were turned around and were 
pushing the satellite along. How 
can that be? 

7 12 through 1 16. 

44 The flying circus of physics 

Heat fantasies and 
other cheap thrills 

of the night 


(3.1 through 3.9) 

Boyle's law 

partial pressure 

atmospheric and water pressure 


The well-built stewardess 

happens to a stewardess wearing 
an inflatable bra when the cabin 
of her jet plane is depressurized? 

Just what you're thinking, 
Herman. Inflation. 

As Los Angeles Times columnist 
Matt Weinstock told it Friday, this 
set of potentially explosive cir- 
cumstances occurred recently on a 
Los Angeles-bound flight. He 
gallantly withheld the identity of 
girl and airline. 

"When she had, ahem, expanded 
to about size 46," Weinstock wrote, 
"she frantically sought a solution. 
Somehow she found a woman 
passenger who had a small hatpin 
and stabbed herself strategically. 

"However, another passenger, 
a man of foreign descent, mis- 
understood. He thought she was 
trying to commit hara-kiri the 
hard way. He grappled - with her 
trying to prevent her from 
punching the hatpin in her chest. 

"Order was quickly restored, but 
laughter still is echoing along the 
the airlines." 
Weinstock says it really happened. 

Exceptionally good reference: Chem- 
ical Principles Exemplified," edited and 
written by R. C. Plumb, monthly in J. 
Chem. Ed. 

Good thing they don't make 
these bras puncture-proof. 
. . .Associated Press 

Can you calculate the stewardess's 
pectoral measurements as a func- 
tion of altitude? 


Making cakes at high altitudes 

Why does the recipe for a cake 
change when you do the baking 
above 3500 feet? The side of the 
cake mix box calls for more flour, 
more water, and a higher baking 
temperature when the mix is 
used at altitudes greater than 
3500 feet. 

316, pp. 184-186. 




The Swiss cottage barometer 

One of my grandmother's most 
fascinating possessions is her Swiss 
cottage barometer. She explains 
that when the pressure falls, a little 
man comes out of the cottage to 
warn of a coming storm. During 
fair weather a little woman 
comes out instead. How does this 
cottage barometer work, and does 
it actually measure the barometric 
pressure? I notice that when I 
place it in the bathroom it pre- 
dicts bad weather far more often. 
Why the increase in frequency? 



Wells and storms 

My grandmother claims that during 
storms her water well is easier to 
pump but the water may be unfit 
to drink because of an increase in 
suspended matter. This happens, 
she says, whether the storm brings 
rain or not. Others have noticed 
that artesian wells generally in- 
crease in strength during storms, 
again regardless of the rain. Why 
would these wells respond to 
storms? Might there be an op- 
posite effect in which a normally 
freely flowing well is stopped? 

318 f p. 143. 


surface tension 


One balloon blowing up another 

Blow up two identical balloons, 
one more than the other. Take 
care that air doesn't leak until 
you've joined the two balloons by a 
short length of tubing as shown in 
Figure 3.5. What will they do 
when they are joined? Does the 
smaller balloon expand at the ex- 
pense of the larger one? Intuition 



s 4 


Figure 3.5 

46 The flying circus of physics 

may say yes, but actually the op- 
posite happens: the smaller bal- 
loon shrinks and the larger balloon 
expands. Why? The same phenom- 
enon occurs with soap bubbles. 
See Boys's soap bubble book (322). 

321; 322, pp. 56-57. 


Emergency ascent 

Suppose that while scuba diving 
at some great depth, say 100 feet, 
you had to make an emergency 
ascent without additional air. One 
lungful has to be enough for you to 
reach the surface, or you 11 die. 
How would you do it? (This is not 

Boyle's law 

partial pressure 


Champagne recompression 

When a tunnel under London's 
Thames River had been completed 
and the two shafts had been joined, 
the local politicians celebrated 
the event at the tunnel's bottom. 
In the tunnel they unfortunately 
found the champagne flat and life- 
less. When they returned to the 
surface, however, "the wine popped 

in their stomachs, distended their 
vests, and all but frothed from 
their ears [Figure 3.6] . One digni- 
tary had to be rushed back into 
the depths to undergo champagne 
recompression " (314). What 
happened to the politicians? 

314; 315. 

Figure 3.6 

The danger of subterranean champagne. 

really just an academic question, for 
submarine crews are trained to make 
such emergency escapes.) Would 
you continuously release air as you 
ascend, or keep it all in? Well, 
although it may seem unreasonable, 
you had better release air or you 
won't make it. In fact, novice 
scuba divers practicing in swimming 
pools are occasionally killed because 
they neglect to exhale when prac- 
ticing emergency ascents. Why? 

It is said the urge to take another 
breath stems from the partial pres- 
sure of the C0 2 in your lungs, not 
the volume of the C0 2 . Researchers 
conclude from this that the most 
dangerous and crucial point in your 
ascent will be at some intermediate 
point and not near the surface. 
Once you pass the crucial point, 
the urge to take another breath will 
relax considerably. Why is this? 
What is the crucial depth? How 
fast should you swim to the sur- 
face? Can you swim too fast? 
If you can, then what's a reason- 
able rate? 

325 through 328. 



You'd probably imagine that caves 
are full of stagnant air. Some are, 
but at the entrances of some, called 
"blow-holes" by spelunkers, a 
fierce wind blows constantly. Why 
is that? Even stranger are the 
breathing caves where the air blows 
in for a moment and then out al- 
ternately. What drives the air back 
and forth? 

318, pp. 143-144; 319; 320. 

Heat fantasies and other cheap thrills of the night 4 7 


Decompression schedule 

In deep-sea-diving ascents there 
is always the serious threat of 
"bends," in which bubbles form 
from the nitrogen dissolved in 
the tissue during the dive. This 
can be not only painful but 
also paralyzing and even fatal. 
Consequently, the ascent is 
made slowly enough that the 
nitrogen is disposed of without 
bubble formation. You have seen 
this in movies: the diver stops at 
various depths in his ascent. 
Where do you think the longest 

stop is: near the surface where 
the diver is almost at atmospheric 
pressure, near the bottom, or at 
some intermediate point? I 
would have eliminated the first 
choice immediately, but the 
decompression schedule in 
Figure 3.9 contradicts me: the 
longest stops are near the sur- 
face. Why should that be? What 
is the deepest dive you can take 
without having to wait around 
on the way up? 

323; 324. 







Figure 3.9 

Decompression schedule as recommended by the U.S. Navy for 
a one-hour dive at 200 feet. Dashed line indicates the sea-level 
pressure. [After H. Schenck, Jr., Amer. J. Phys., 21, 277 (1953).] 

Thermal expansion 
& contraction 

3.10 through 3.15 


Hot water turning itself off 

When I turn on the hot water in 
my sink, the water's flow rate 
slowly decreases and the flow may 
even stop. The cold water won't 
do that, so why does the hot 
water behave so badly? Why does 
it do that only when I've first 
turned it on and not the second 
time, after I've turned it up? 

thermal expansion 


Bursting pipes 

Why do water pipes burst in winter? 
If the only thing that occurs is the 
freezing of water next to the pipe 
walls, then there shouldn't be any 
great strain on the pipe and hence 
the pipe shouldn't burst. Besides, 
the bursting usually occurs away 
from the point where the water 
is frozen. So, again, what causes 
the burst? Is there any real ad- 
vantage in letting outside taps 
drip all winter as some people 
do? Finally, is there any 
truth to the common idea 
that hot water pipes burst far 
more often than cold water pipes? 

253, pp. 136-137; 338, pp. 
35-36; 339. 

48 The flying circus of physics 

Figure 3.12 


Fever thermometer 

When you take your temperature, 
the heat of your mouth makes the 
mercury expand. Why doesn't the 
mercury level fall as soon as you 
remove the thermometer from 
your mouth? It doesn't, because 
a constriction in the tube prevents 
it from falling (Figure 3.12). But 
why? After all, during the expan- 
sion the mercury passed through 
the constriction. Why won't it 

do the same during the contrac- 

Why does the reading drop for 
a moment if you stick the 
thermometer into hot water? 
(Don't overheat the thermometer 
so that it breaks.) 

160, p. 114; 31 7, pp. 117-118, 
129; 329, p. 50; 330, p. 4 1; 33 1, 
p. 6. 


Heating a rubber band 

Stretch an uninflated balloon and 
then touch it to your face. It 
feels warm. Now let it contract to 
its normal size. It feels cool. Why? 
If you heat a rubber band it con- 
tracts. Why is its behavior precisely 
opposite that of metal? What's 
different about its structure? Figure 
3.13 shows a rubber-band engine 
based on this property. The spokes 
of the wheel are rubber and hence 
will shrink when heated. The wheel 
turns because of the shift in the 
center of gravity. 

155, p. 244; 332, Vol. 1, p. 44- 1, 
333 through 337. 

Figure 3.13 

A rubber-band heat engine. 
(Reprinted by special permission 
from Feynman, et al, The 
Feynman Lectures on Physics, 
Vol. 1, 1963, Addison-Wesley, 
Reading, Mass.) 


Watch speed 

Since metal expands when it's 
heated and a watch spring is metal- 
lic, wouldn't you think that a 
watch would run at different speeds 
in cold and in warm weather? 

9, p. 82; 160, p. 125; 31 7, p. 
129; 329, p. 43; 330, p. 90; 
331, p. 23. 


nonlinear oscillations 


U-tube oscillations 

If a U-tube of water is heated and 
cooled as shown in Figure 3.15, 
the water will begin to oscillate 
from one side to the other. (There 
must be open reserviors with the 




Figure 3.15 

The water will oscillate from side 
to side if the tube is heated and 
cooled as shown. [After P. 
Welander, Tellus, 9, 419 (1957).] 

Heat fantasies and other cheap thrills of the night 49 

air-water surface area larger than a 
critical size.) The change in water 
levels can be a millimeter or so, and 
the period of the oscillations can 
range from about 20 seconds to 4 
hours depending, in part, on the 
cross-sectional area of the U-tube. 
Doesn't the symmetry of the situa- 
tion make it seem curious that 
the water oscillates? What first 
starts the oscillation and what 
parameters determine its period? 


adiabatic process 


Bike pump heating up 

Why does the valve on a bicycle 
pump get hot when you're 
pumping up a tire? Is it because 
of friction from the air being 
forced through the valve? Well, 
perhaps, but if you use a gas 
station's compressed air supply, 
the valve usually doesn't get hot. 




West-slope hill growth 

Why is it that in the United States 
there is often more vegetation on 
the westward slopes of hills and 
mountains than on the eastward 
slopes? You may even find extreme 
cases where the east side is bar- 
ren though the west side has thick 

360, pp. 162-165. 

adiabatic processes 


The Chinook and going mad 

The Chinook is a warm, dry wind 
that blows down from the 
Rockies into such places as Denver 
(Figure 3.18). It can be up to 
50 F above the ambient tempera- 
ture and may reach speeds as 
high as 80 mph. The mystery is 
how a warm wind could come 
down off a cold mountain. Be- 
sides, warm air should rise, 
shouldn't it? Legend says the 
warmth comes from the ghosts 
of Indians buried in the moun- 

Chinook-like winds are by no 
means confined to the Denver 
area. In Switzerland this wind 
is called the foehn; \n Ceylon, 
the kachchan; in South Africa, 
the berg wind; in Southern Califor- 
nia, the Santa Ana; and in other 

v Mountains ;.# 




places, other names. They all 
share the properties of being dry 
and warm. 

They also share a very con- 
troversial feature, namely, it is 
said that they drive men and 
animals mad. When these winds 
blow, crime rates increase, rape 
and murder are more frequent, 
there are more traffic accidents, 
and people just act generally more 
irrational. This could be an old 
wives tale, or there could be 
some truth in it. How could dry, 
warm winds affect a man physio- 
logically? Is there any physical 
reason for the irrational behavior? 

164 f pp. 217-218; 343 f p. 348; 
344 , pp. 94-98; 345 through 


Figure 3.18 

The Chinook wind blowing down off the Rockies. 

50 The flying circus of physics 

adiabatic process 


Coke fog 

Have you ever noticed the thin fog 
that gathers at the mouth of a 
chilled champagne or soda bottle 
just after it's been opened (Figure 
3.19)? What causes the fog? 

342. /rfe 

Figure 3.19 

Fog at mouth of freshly opened, 

chilled champagne bottle. 


Convertible cooling effect 

On a hot day you're in luck if you've 
got a friend with a convertible. 
Driving down the road with a good 
breeze always does the trick against 
the heat. You feel cooler but a 
thermometer should read the 
same with or without a breeze, 
shouldn't it? Try it. With a ther- 
mometer in the back seat, measure 
the temperature when the car is 
parked and when it is moving. 
You'll probably find that the 
thermometer reads about 1/2° C 
lower when the car is moving. Why': 


adiabatic process 

radiation absorption 


Death Valley 

Death Valley is both the lowest 
point on the American continent 
and the hottest place in the 
world. Temperatures there may 
be as high as 120°F for several 
days straight, and once a tempera- 
ture of 134°F was recorded. 
Isn't there something physically 
wrong in its being so hot if it is 
so low? Since hot air rises and 
cold air sinks, and since the 
valley is surrounded by mountains 
with cold air on their tops, 
shouldn't the valley be a relatively 
cool place? 

223 \ p. 200. 

adiabatic process 


latent heat 



Mountain top coldness 

Why are mountain tops cold? Isn't 
the solar heat per unit area on a 
mountain about the same as at sea 
level? And shouldn't cold air sink? 



adiabatic process 


Holding a cloud together 

What holds a cloud together? Or, 
on partially cloudy days why are 
some parts of the sky cloudy and 
others not? Wouldn't you expect 
a more uniform distribution of the 
clouds over the sky? 

363, pp. 44-67; 365. 


Mushroom clouds 

Why do ground-level nuclear and 
other large explosions leave mush- 
room clouds? 

371, pp. 202-203; 372; 373. 

cloud genesis 




Holes in the clouds 

Mysterious circular holes have oc- 
casionally been observed in other- 
wise uniform cloud banks. The 
feeling is that these holes, which 
are usually quite large, are not just 
random arrangements of the clouds. 
Suggestions as to their cause have 
ranged from burning meteors to 
accidental or intentional cloud 
seeding. How exactly could any 
of these explanations account for 
such holes? 

362, p. 9 1; 374 through 379. 

Heat fantasies and other cheap thrills of the night 5 1 

cloud genesis 



Figure 3.26a 

Two types of mountain peak clouds. 


Mountain clouds 

If you have ever lived near moun- 
tains you may have noticed the 
stationary clouds often found over 
mountain peaks. Two are shown 
in Figure 3.26a. What causes these 
formations? The wavelike series of 

Figure 3.26b 

Wavelike clouds associated with a mountain peak. 

clouds that sometimes occurs near 
a peak is even more intriguing 
(Figure 3.265). What determines 
the spatial periodicity of these 

164, pp. 301-303; 360, pp. 86- 
88; 361, pp. 14-21,39; 362, 
pp. 64-73; 363, pp. 75-82; 364, 
pp. 229 ff; 365 through 370. 

shock wave 






Spherical cloud of A-bomb blast 

In some circumstances, a nuclear 
blast is accompanied by a thin, 
spherical cloud (Figure 3.27). 
What causes these clouds? How 
fast do they expand? Will they 


significantly reduce the radiation 
produced by the explosion? 

219, pp. 31 1-312; 371, pp. 
34 ff. 

Figure 3.27 


Burning off clouds 

When there were low-hanging clouds 
on an early summer morning, my 
grandmother would often say 
the sun would "burn them off" and 
the day would be sunny. Since they 
did often disappear later in the 
morning, I figured she was right and 
that the sunlight absorbed by the 
clouds indeed "burned them off." 
Was I correct? 

363, p. 76; 364, pp. 273-274. 

52 The flying circus of physics 

cloud genesis 





What causes the breastlike cloud 
structure called mamma (Figure 
3.29)? In particular, why are there 
sometimes bright gaps between 
the mammae? 

362, pp. 54-56. 

Figure 3.29 

Mamma cloud formation. 



Cause of fog 

London's fogs have diminished in 
intensity in the last decade partial- 
ly because there was a reduction in 
the use of open coal burning. 
What has open coal burning got to 
do with fogs? In general, what 
causes fogs? 

388, pp. 480-510. 


Breath condensation 

Why does your breath condense 
on the window pane on a cold 
day? More specifically, what 
actually causes the water mole- 
cules to form into a drop? Why 
did those water drops condense 
in those particular places on the 
glass. . .what was so special about 
those places? 

Why does a hot piece of toast 
leave moisture on a plate? 

388, pp. 428 ff; 389. 

bubble nucleation 


Salt water bubbles 

Why are more bubbles produced 
when salt water is poured into 
salt water than when fresh water 
is poured into fresh water? 



adiabatic process 



Contrails and distrails 

Why do contrails often form behind 
airplanes? Why aren't they always 
produced? If you look closely you 
may see that a contrail actually con- 
sists of two or more streams that 
eventually diffuse and become in- 
distinguishable. Why is there more 
than one stream at first? Why is 
there a clear gap between the air- 
plane and the leading edge of the 
contrail? What's responsible for 
the bursting and blooming of 
contrails that makes them look 

like strung popcorn (Figure 3.32). 

You may be fortunate enough 
to see both a contrail and its 
shadow on underlying clouds. But 
the dis trail, a dark line left by an 
airplane flying through a cloud, is 
even more interesting. How does 
an airplane make that kind of 

362, pp. 120- 129; 364, pp. 73- 
74; 380 through 387; 1537. 

Figure 3.32 

Side view of contrail that has burst to a popcorn appearance. 

Heat fantasies and other cheap thrills of the night 53 

Bernoulli's principle 


Fireplace draft 

In a good fireplace the smoke goes 
up the chimney rather than out 
into the room, even if the fire is 
not directly beneath the hole. What 
causes this draft, and why is it 
better the taller the chimney? 
Why is the draft better on a windy 
day? Finally, why do some 
chimneys puff (Figure 3.34)? 

44, p. 188; 3 18, pp. 225-230; 
364, pp. 2 16-217; 39 1, pp. 1 1 1- 
112; 392, pp. 108-112; 393; 394. 

Figure 3.34 
Puffing chimney. 



Open-air fires 

Many communities that still allow 
open-air fires forbid them during 
the daylight hours. Why would it 
matter whether the fires are during 
the day or evening? 







A Fellow docsw't MIND 



By permission of John Hart. Field Enterprises 


turbulent eddies 


Cigarette smoke stream 

Why does cigarette smoke suddenly 
form swirls after rising smoothly 
for several centimeters (Figure 

399, pp. 175-176; 400. 

Figure 3.36 

54 The flying circus of physics 




free energy 

lapse rate 


Freezing water 

Why does water normally 
freeze at 0°C? What is so special 
about that particular tempera- 
ture? Under some circumstances 
liquid water can exist at subzero 
temperatures; for example, water 
drops at temperatures as low as 
— 30° C have been found in clouds. 
What must be done to make such 
supercooled water? 

Can ice be heated above 0°C 
without melting? 

338; 389; 402 through 404. 


Stack plumes 

You would think an indus- 
trial stack plume would rise 
vertically or, if there is a wind, 
would rise at some angle. Yet 
the plume shapes shown in 
Figure 3.37a are often seen in 
a uniform horizontal wind. What 
causes these shapes? The last 
one with the peculiar periodicity 
is especially interesting. Why do 
some bent-over plumes split 
sideways downwind from the 
stack (Figure 3.37b)? 

364, pp. 207-212; 395 
through 398. 


Figure 3.37b 

Top view of a bent-over plume 

that has been split sideways. 

(uniform and of reasonable speed) 



latent heat 


Figure 3.37a 

[After Bierly and Hewson, J. 

Appl Meteorology, 1, 383 (1962), 

permission granted by authors 

and the American Meteorological 



Freezing hot and cold water 

In cold regions like Canada or 
Iceland, it is common knowledge 
that water left outside will freeze 
faster if it is originally hot. While 
this may seem completely wrong 
to you, it is not just an old wives' 
tale, for even Francis Bacon 
noticed it. Try putting warm and 
cool water in various containers 
either outside on a freezing night 
or in your freezer. If in any of 
your tests the warm water freezes 
first, then you'll have to explain 

405 through 411. 

ice crystal growth 


radiation absorption 


Shades of ice coverings 

If you observe a distant ice 
covering on a North Alaskan 
lake or river when it begins to 
melt in the late spring, large 
parts of the ice will look dark 
and other parts will look white. 
A walk across the ice can quickly 

(and painfully) teach you that 
the dark ice is weaker and should 
be avoided. Why is the ice light 
and dark, and why are the dark 
areas weaker? 

338 », pp. 120-126; 376. 

Heat fantasies and other cheap thrills of the night 55 

thunderstorm thermodynamics 

density change with temperature 


120 g 

Hours, GMT 



Figure 3.41 

(After D. J. Malan, Physics of Lightning, English Universities Press, Ltd.) 


Worldwide thunderstorm activity 

If you plot the worldwide thunder- 
storm activity versus Greenwich 
Mean Time (GMT), you get a curve 
that has a maximum at 7 P.M. 
London time and a minimum at 
4 A.M. London time (Figure 3.41). 
In other words, when it is 7 P.M. 
in London, the earth is experiencing 

the greatest amount of thunder- 
storm activity. Is any time depen- 
dence plausible? Is there any 
physical basis for this particular 

219, pp. 123-124; 300, pp. 
109-11 1; 332 \ Vol. II, Chapter 
9; 388, p. 445,401. 

heat conduction 


Getting stuck by the cold 

If you touch a cold piece of metal 
such as a metal ice tray fresh from 
the freezer, your hand may stick 
to the metal. Be careful if you 
actually try this experiment, for 
you can lose the skin that sticks to 
the metal. Have water running in 
your sink and, immediately after 
touching the ice tray, dunk your 
finger and the tray under the water. 
Do not lick the tray, as some 
unknowing children do, for that 

may result in very painful injury. 

Why does your finger stick to 
the tray? How cold must the 
metal be for this sticking to 

latent heat 


Wrapping ice 

Why does ice keep frozen longer 
if it is wrapped in a wet piece of 

160, p. 166. 



Pond freeze 

Why does the top of a pond freeze 
before the middle and long before 
the bottom? (There's more than 
one reason.) If this weren't so, 
there would be virtually no fresh- 
water fish outside the tropics. 

In areas where water transporta- 
tion is necessary, the formation 
of ice can be prevented by bubbling 
air up from pipes laid on the bot- 
tom of the lake or river. If ice is 
already present, the bubbles will 
even melt the ice although it may 
take four or five days to do it. 
How do the bubbles clear a river 
or lake in this way? 

158, p. 288; 403; 4 12, pp. 495- 
496; 4 13, p. 139; 4 14, pp. 4-6, 


phase change 




What allows skis to glide over 
snow? Is it the same as the mech- 
anism involved in ice skating? 
Could you ski on other frozen 
substances or is snow (water) 
unique? Can it get too cold to 
ski? Why are skis waxed? Finally, 
why do ebonite skis slide much 
better than metal ones? 

421, p. 393; 422 through 424. 

56 The flying circus of physics 

adiaba tic compression 

pressures and phase change 


Ice skating 

When you are ice skating, why do 
your skates slide along the ice 
surface? If you can, explain the 
physics involved with practical 
numbers. Obviously it can get too 
warm to skate. Can it get too cold? 

Is the ice that is found in very cold 
places, such as Greenland, slippery? 
Could you skate in a similar way 
on other frozen materials such as 
carbon dioxide (dry ice)? Suppose 
you had to walk across ice and you 
could choose between a patch of 
smooth ice and a patch of rough 
ice. Would you find one more 
slippery than the other? 

166; 321, p. 274; 4 14, pp. 1 1 1- 
113; 418, p. 129; 419; 420. 


phase change 


Making a snowball 

Why can't you make a snowball if 
the temperature is very low? What 
holds a snowball together, anyway? 
Approximately what is the lowest 
temperature at which you can still 
make a reasonably good snowball? 


adiabatic compression 

pressure and phase change 


Snow avalanche 

How can sudden warmings and 
mechanical vibrations trigger 
snow avalanches? Why do many 
avalanches occur at sunset when 
there is a general cooling rather 
than a warming? There are 
even claims that a skier's shadow 
may be enough to set off an 
avalanche. Why would this happen? 
In a dry snow avalanche a huge 

cloud of snow particles precedes 
the slide, crashing down the 
mountain side at speeds up to 200 
miles per hour with enough force 
to destroy large trees and move 
steel bridges. According to one 
story about a skier caught in 
one of these snow slides (Figure 
3.47), the skier and the slide 
reached the opposite slope with 

such speed that the trapped air 
was compressed and warmed and 
thus partially melted the snow. 
Within several minutes, how- 
ever, the snow had refrozen, 
and when the rescue team reached 
the still-living skier, they had to 
saw him out. 

415 through 417. 


Figure 3.47 

Heat fantasies and other cheap thrills of the night 57 


phase change 


Snow tires and sand for ice 

Sand and studded snow tires are 
both commonly used in winter 
driving on icy streets. Why is 
it that neither does you much 
good if the temperature is below 
zero? For that matter, why do 
they help for temperatures above 


freezing point 


Salting ice 

When my grandmother makes home- 
made ice cream, she packs ice 
around the ice cream container, 
and then she salts the ice. Why does 
she add the salt? In a similar vein, 
why is salt put on icy roads? To 
both these questions you'll proba- 
bly answer, "to lower the freezing 
point." Yes, but how does salt 
lower the freezing point? If the 
day is very cold, the salt won't im- 
prove the road contions. What is 
the lowest temperature at which 
it will still do some good? 

How cold would it have to be for 
a body of salt water to freeze 

4 13, pp. 187- 188; 4 14, pp. 3-4, 

freezing point 


Antifreeze coolant 

Why does a mixture of antifreeze 
and water freeze at a lower tem- 
perature than pure water? How 
does the antifreeze also provide 
protection against overheating 
in the summer? If antifreeze is 
so good in these respects, then 
why don't you completely till 
the radiator with it and forget 
about the water? (Most anti- 
freeze manufacturers suggest 
the mixture should not exceed 
about 50% antifreeze.) 

330, pp. 227-228. 

latent heat 


Feeling cool while wet 

Why do you feel cool when you 
first step out of a shower or a 

pool? Try to estimate your rate 
of heat loss. (One parameter now 
used to measure such a cooling ef- 
fect in a wind is the windchill fac- 

Why are hosptial patients some- 
times given methyl alchohol rub- 
downs to soothe them? Why not 
just use water? 

When I was young and on vaca- 
tion with my family, we kept a 
canvas water bag on our car's front 
fender. Though the day may have 
been hot, the water in the bag was 
always cool. Why was that? Can 
you calculate the temperature of 
the water for some given situation 
(air temperature, humidity, car 

158, p. 324; 427, p. 64; 428; 

freezing point 


Carburetor icing 

On some days, even when the tem- 
perature outside is as high as 40° F, 


58 The flying circus of physics 

my carburetor will ice up and cause 
my car to stall. Figure 3.53 shows 
the throttle plate being frozen in 
place, thereby stopping the air 
flow to the engine. What causes 
this icing? Is this more likely on 
a dry or on a humid day? Can it 
happen when the outside tem- 
perature is below freezing? 


Figure 3.53 
Carburetor icing. 

latent heat 



Eating polar ice 

Eskimos know that newly frozen 
sea ice is much too salty to eat 
or to melt for drinking but sea 
ice several years old is fine. They 
have also found that if the ice 

is pulled up onto shore and out 
of the water, the desalting is 
speeded up, especially if this 
is done during the warm spring 
and summer months. Why does 
the salinity decrease with time 
and, in particular, why does it 
decrease faster in the warm months 
when there should be more evapora 
tion and a resulting Increase in 

338, pp. 95-97; 4 14, pp. 26- 
28; 425. 

latent heat 


A pan top for boiling water 

If you boil a pan of water for 
spaghetti, why does the boil 
come much faster if the lid is 
left on? Well, there is less heat 
loss, right? But what does 
that really mean? Is there less 
convection or less infrared radia- 
tion? When the lid is on, isn't the 
lid itself nearly at the boiling tem- 
perature? Hence, won't there be 
nearly as much radiation and con- 
vection above it as above an open 
pan? If so, why does the water 
boil faster in a covered pan? 


latent heat 


Briefly opening oven 

My grandmother claims that on 
humid days her oven heats up faster 

if she opens the oven door wide 
and then closes it just before she 
turns on the heat. If this is true, 
then explain it. 

160, p. 174. 

latent heat 


Water tub saving the vegetables 

My grandmother puts a large pot 
of water in the cellar near her 
vegetables to protect them from 
frost. Why would the presence of 
the water help protect the 

160, p. 161; 329, p. 70; 438. 

latent heat 


Icehouse orientation 

Before the refrigerator was in- 
vented, people in northern climates 
would store winter ice in icehouses 
for use in the summer. Among the 
features required of a good icehouse 
was proper orientation: its door- 
way had to face towards the east 
so the morning sun would eli- 
minate the damp air. But this also 
meant the sun would warm the 
icehouse more than if it faced 
north or south, and so the damp- 
ness must have been far more un- 
desirable than the extra warming. 
Why was that? 


Heat fantasies and other cheap thrills of the night 59 

heat conduction 

heat pipes 

latent heat 


Heating meat with a "Sizzle Stik" 

How can you get a roast to cook 
faster? Well, you can stick a 
metal rod into it as is commonly 
done in baking potatoes. Since 
heat is then conducted into the 
meat's interior quicker than 
directly through the meat, the 
meat cooks much faster. There is 
a device called the "Sizzle Stik"*, 
however, which abandons the metal 
rod in favor of a hollow metal 
tube containing a wick from end to 
end and some water (Figure 3.59). 
It is claimed that heat conduction 
is 1000 times better than with 
the solid tube, and indeed, cooking 
times may be cut in half. But 
how? Why would a hollow tube 
like this be better than a solid 
one? And why is there water and 
a wick in the hollow tube? 

430 through 432. 

Figure 3.59 

Sizzle Stick* in roast (After 

drawing by Horizon Industries.) 

*® Horizon Industries, Lancaster, Penn- 
sylvania 17601, U.S.A. 

pressure and phase change 

latent heat 


The highest mountain 

On the earth why aren't there 
any mountains significantly higher 
than Mt. Everest, say, ten times 
higher? (Nix Olympica on Mars is 
over twice as high as Mt. Everest.) 
If there is some limit to mountain 
heights, then what determines it, 
and approximately what is the 




The boiling water ordeal 

One of the most fascinating 
examples of Oriental magic is the 

Yubana, or boiling water ordeal, 
of the Japanese Shinto following. 
In the Yubana, the performer 
approached a huge caldron 
filled with boiling water and 
suddenly thrust two clumps 
of bamboo twigs into the 
liquid, flinging it high and 
showering it all about his 
head, shoulders and arms. 
As the water reached the 
fire below the caldron, it 
produced great clouds of 
steam, which subsided 
only when the caldron 
was almost empty. The 
performer was then seen 
quite unharmed by the 
ordeal, proving the 
v mighty power of Shinto.* 
Boiling water would have burned 
the performer's skin, of course, so 
there must have been some trick. 
Hence, you should not try this 
experiment yourself. Would it 
have helped if the Shintoist timed 
his ritual so that his feat came soon 
after boiling commenced? What 
was the water temperature then? 


*From Master Magicians by Walter 
Gibson, Copyright © 1966 by Walter 
Gibson. Reprinted by permission of 
Doubleday & Company, Inc. 

phase change 

latent heat 

bubble formation 


Boiling point of water 

What does it really mean to say that 
a pan of water is boiling? One 

60 The flying circus of physics 

hundred degrees centigrade is the 
commonly accepted boiling point 
of water at an atmospheric pres- 
sure of one atmosphere. How can 
any one temperature like this be 
called the boiling point? Why can 
water sometimes be heated above 
100°C without boiling (still at a 
pressure of one atmosphere)? 
Finally, why is it claimed that 
once water has reached 100°C any 
additional heat input will not raise 
the water's temperature but will 
only increase the evaporation rate? 
Why can't the water beneath the 
surface get hotter than 100°C with 
an additional heat input? 


evaporation rate 


A puddle's salt ring 

When salt has been used to deice a 
sidewalk, why is it left behind in 
rings around the puddles as the 
puddles evaporate? The same thing 
can be seen on a larger scale in 
the white edges around lakes in 
dry areas. You can even see it 
in your own kitchen by saturating 
a glass of hot water with salt and 
then letting the solution set for a 
month. Afterwards, both the 
inside and outside surfaces of 
the glass will be coated with salt. 
Why is salt left on the outside of 
the glass? 

360, pp. 21-23; 458. 

ideal gas law 

vapor pressure 

latent heat 

phase change 


Dunking bird 

The dunking bird, which is 
probably the most popular of all 
physics toys, is a glass bird that 
rocks back and forth and "drinks" 
from a glass of water (Figure 
3.64a). You start the motion by 
wetting the head, after which the 
bird slowly begins to oscillate and 
eventually dunks its head into the 
water. The bird then rights itself 
and repeats the cycle without 
further assistance. As long as it 
keeps getting its head wet, it will 
continue to bob up and down. 
What makes it go? 

Perhaps the dunking bird is a 
solution to next century's power 
needs. Just imagine— we erect a 
huge bird just off California, and 
as it continuously dunks its head 
into the ocean, it provides the 
entire West Coast with energy. 

Figure 3.64a 
Dunking bird. 

This might lead to a dunking- bird 
cult, however, and we would all 
end up paying tribute by dunking 
in unison three times to the west 
each morning (Figure 3.646), so 
maybe we'd better just forget it. 

433 through 437; 1457. 

Figure 3.64b 

The dunking-bird cult. 

Heat fantasies and other cheap thrills of the night 61 

vapor pressure 

steam flash 



Dancing drops on hot skillet 

If water drops are sprinkled onto 

The drop is actually vibrating 

x / 

a dry, hot skillet, the drops will 
dance and skim along the skillet's 

but since your eye cannot follow 
the motion that quickly, you see 



surface. Why don't the drops 

a composite shape. To catch it 

^ s ^^:^^^Xateh basin 

evaporate immediately? What 

in various vibrating states, use a 


makes them skim along? Sur- 

stroboscope or a high-speed 


prisingly enough, the drops will 

camera. In Figure 3.65 some of 


disappear faster if the skillet is 

the fundamental shapes are sketch- 

: = : 

Iron pipe 

cooler. Why is that? 

Examine a skimming drop 
closely and you will find it 
assumes a variety of odd shapes. 

ed. Why do the drops vibrate? 

155, p. 234; 160, pp. 171-172; 
330, p. 254; 442 through 446. 



!Ei Continuous 

t ^ heater 

Figure 3.66 

Artificial geyser. (E. Taylor after 

F. I. Bo ley.) 



What causes the eruptions of 

geysers and, in Old Faithful's 

case, what is responsible for the 

periodicity of the eruptions? 

Could their energy source be 

simple heat conduction through 

the surrounding rock, or is a 

faster heat supply needed? 

Suppose you were to make an 

artificial geyser with a continuous 

heat source as shown in Figure 3.66. 

How deep should you make the 

tube, how much power should you 

provide for the heating, how often 

would it erupt, and how high would 

the water jump? 

Figure 3. 65 

450 through 452. 

[After N. J. Holter and W. R. Glasscock, J. Acoustical 

Soc. Amer., 24, 682 (1952).] 

62 The flying circus of physics 

vapor pressure 



How does my plain old, non- 
electric coffee percolator work? 
For example, must the central 
stem be relatively small? And, is 
all of the water at boiling tempera- 
ture when the pot begins to perk? 

253, pp. 110-111; 1533. 

latent heat 


Single-pipe radiators 

While most steam radiators have 
two pipes (one inlet and one outlet), 
there is one system in which there 
is only a single pipe (Figure 3.68). 
As if that were not strange enough, 
it is said that the steam and return- 
ing water in that single pipe are at 
the same temperature. How could 
they be at the same temperature 
if the radiator is heating the room? 
Where does the radiated heat come 

318, pp. 6-8; 418, p. 143. 



Figure 3.68 


Licking a red-hot steel bar 

Though fire walking has long been 
associated with Far East mysticism, 
there have recently been some 
scientific investigations into the 
feat and even a fire-walking dis- 
play before thousands of people 
at a soccer match half time. Even 
more amazing than the fire walkers, 
however, are those people who 
can briefly plunge their hands into 
molten metal and touch and lick (!) 
red-hot steel bars without the 
slightest injury. You may suspect 
deceit is involved, but the feat can 
actually be explained with good 
physics. Although I have dipped 
my fingers into molten lead with- 
out harm, you should not try these 

experiments yourself, for they are 
dangerous and can result in a very 
bad burn. Figure 3.69 shows that 
even good physics won't save an 
overconfident scientist. 

Suppose a professional showman 
were to lick a red-hot steel bar. 
What might guard his tongue not 
only from a very serious burn, but 
indeed from any burn at all? Why 
should he use only extremely hot 
metal? Is there any danger in less 
hot metal? In fire walking is there 
any optimum speed with which to 
walk? In particular, can a fire 
walker walk too fast? 

330, pp. 254-255; 447; 448. 

Heat fantasies and other cheap thrills of the night 63 

steam flash 



Banging radiator pipes 

What causes the hammerlike 
pounding of steam radiators? 

253, p. 155; 318, pp. 9, 15; 453, 
p. 319. 

thermal absorption 



Wrapping food with aluminum 

Ordinary kitchen aluminum foil 
has one shiny side and one dull side. 
Does it really matter which finish 
is on the outside when the foil is 
wrapped around something to be 
cooked, as a baked potato for 
example? Which finish should be 
outside when the wrapped material 
is to be frozen, and again does it 
really make a difference? 


Old incandescent bulb 

Why does an incandescent bulb be- 
come gray as it becomes old? Does 
it become uniformly gray, or is 
one side preferred? 


How hot is red hot? 

Probably you know that an ob- 
ject sufficiently heated will become 
incandescent. A red-hot poker 
in the fire is a common example. 
Can you estimate the temperature 
at which an object, let's say, the 
poker, first becomes visibly in- 
candescent? Does it matter if the 
poker is black iron or shiny steel? 


Figure 3. 74 
Refrigerator as an air 


Cool room with refrigerator 

Once, on a very hot day, I tried to 
cool my dorm room by leaving my 
refrigerator door open (Figure 
3.74). How much did I cool my 
room that way? 

64 The flying circus of physics 

thermal absorption 


and transmission 

nonlinear oscillation 


Black pie pans 

Why are the bottoms of some 
frozen pie pans painted black? 

If you make a pie yourself and 
you want the bottom crust 
browned, why should you use a 
thermal glass pan rather than a 
metal one? If you have to use a 
metal one, why should it have a 
dull finish, instead of a nice shiny 
one? You may very well already 
know why in principle, but does 
it really matter in fact? Try some 
simple experiments to see. 


Toy putt-putt boat 

The putt-putt boat (Figure 3.77) actually more water is sucked into 

has an unbelievable means of pro- the boiler through the pipes, and 

pulsion. Two pipes join a top sec- the process repeats itself. Thus, 

tion, the boiler, to the boat's rear. the boat putt-putts its way along. 

When the water-filled boiler is Why is water sucked up? When 

heated by a candle, the steam that it is sucked up, why doesn't the 

is produced forces water out of the boat move backward as far as it 

pipes and thus drives the boat for- had previously moved forward? 

ward. The boat should stop when ACA A , . -„ 
* 454 through 457. 
the boiler runs out of water, but 


C Boiler ^ 
<dfc Candle 



Archimedes's death ray 

During the Roman attack of Syra- 
cuse about 214 B.C., the Greek 
scientist Archimedes supposedly 
saved his town by burning the 
Roman fleet with sunlight directed 
by mirrors located on the shore. 
Presumably, many soldiers simul- 
taneously reflected the sun's 
image onto each ship in turn, and 
each ship was set on fire. 

Considering that Archimedes, 
did not have very large mirrors, 
would such a feat be possible? Can 
you estimate how many mirrors, 

Figure 3. 77 

Cutaway view of putt-putt boat. [After I. Finnie and R. L. Curl, 

Amer. J. Phys., 31, 289 (1963).] 

let's say, one meter square, would 
be needed to set aflame dark wood 


specific heat 

100 meters away within less than 
a minute? Should those mirrors 
be curved or flat if the target dis- 
tance is variable? If they are flat, 
how large is the image of the sun 
on the wood? Finally, could 
Archimedes have destroyed the 
Roman fleet in this manner? 

1574 through 1580; 1615; 1616. 


Feeling cold objects 

Shouldn't all objects at the same 
temperature feel like they are at 
the same temperature? You aren't 
reluctant to put your clothes on 
when they are at a room tempera- 
ture of about 70° F, but how about 
sitting down naked in a dry bathtub 
at the same temperature? What's 
the difference? 

462, p. 76. 

Heat fantasies and other cheap thrills of the night 65 

Figure 3.79 

"It's not the heat or the humidity, 
it's this damn 100% wool, fully 
lined burnoose. " 



phase change 


White clothes in the tropics 

Why do people wear white clothes 
in the tropics (if, in fact, they do)? 
Supposedly it keeps them cooler. 
Is that a real and measurable effect? 
If they have light skin, does white 
clothing make any difference? 
Does the sun heat you primarily 
with ultraviolet, visible, or in- 
frared light? How does white 
clothing respond to each of these 
frequency ranges? How much of 
the heating is from direct sun- 
light, and how much is from the 
environment? Finally, if you're 
traversing a desert, should you 
wear white clothing or go nude? 

344, pp. 58-59; 459 through 

thermal conduction 

and absorption 


Cast-iron cookery 

There is an ancient kitchen mys- 
tique about cooking in cast-iron 

pots and pans as opposed to steel 
ones. Cooks, from the gourmet to 
the occasional, swear there is less 
sticking and better, more uniform 
cooking with the cast iron pot. 
Is there any physical basis to that 




thermal conductivity 


The season lag 

Why exactly is it cold in winter and 
warm in summer? Is it because the 
earth is closest to the sun in sum- 
mer and furthest away in winter? 
No, actually just the opposite is 
true (Figure 3.81). 

Predict which months should be 
the coldest and which should be the 
warmest. You will probably pick, 
if your explanation is the common 
one, the months of November, 
December, and January for the 
coldest and May, June, and July 

for the warmest. However, the 
weather records and your own 
experience tell you that the 
coldest months are December, 
January, and February and the 
warmest are June, July, and 
August. As my grandmother 
says, "When the days get longer, 
the cold gets stronger." Why 
does the weather lag your 
prediction by one month? 

388, p. 7. 


June • 

f December 



Figure 3.81 

Earth's orbit around sun (not to scale). 

66 The flying circus of physics 


kinetic theory 



Temperature of space walk 

What is the temperature of the space 
where an astronaut is space walking? 
If he held up a thermometer, what 
would it read? 




A greenhouse is somehow de- 
signed to keep plants in a warm 
environment. How does it do 
this? Does it have special glass or 
will any glass material do? 

A controversial application of 
the greenhouse principle is in 
predicting the results of our 
atmospheric pollution. For ex- 
ample, a catastrophic warming 
of the earth might be caused by 
a high altitude, supersonic trans- 
port system. Why is this feared, 
and how could the more general 
pollution of the atmosphere lead 
to a runaway greenhouse effect? 
The subject is, of course, very 
complicated. In fact, some claim 
that the pollution will not bring 
a warming, but instead will lead 
to a cooling of the earth and 
possibly even another ice age. 
An intriguing account of the 
effects of clouds on the solar 
light input to the earth is in 

Fred Hoyle's excellent science 
fiction book. The Black Cloud 

219, pp. 153- 154; 388, p. 22; 
466, pp. 33-34; 467 through 
469; 1544; 1545. 





Why do you feel cold? 

If you stood naked out in a field 
on a cold winter day, why would 
you feel cold? For instance, is 
your body heat escaping to the 
air by heat conduction? Why 
would a fur coat make you feel 
warmer? Wouldn't it conduct 
heat too? 

While indoors on a cold day, 
stand facing a large window and 
then turn the opposite way. Most 

likely your face will feel cooler in 
the first position. Why is that? 
After all, the air temperature 
doesn't change suddenly as you 
turn around. 

In the movie 2001: A Space 
Odessey an astronaut space 
walked without a spacesuit for a 
few seconds. (The author, Arthur 
C. Clarke, believes this could be 
done without harm to the astro- 
naut.) During such a walk in deep 
space, would the man have a sensa- 
tion of cold? 

How is it that some people can 
adapt to very cold working condi- 
tions? Some people, in fact, court 
an adverse, cold environment for 
religious reasons or to prove their 
stoic nature. An extreme case of 
adaptation was discovered by 
Charles Darwin when he found the 
Yahgan Indians of South America 
living in temperatures near 0°C 
with little more than a fur cape 
draped over their shoulders. What 
physically changes in the body's 

Figure 3.84 

"He was 'streaking." 

Heat fantasies and other cheap thrills of the night 67 

response to the cold to allow such 

Finally, when you do get very 
cold, why do you shiver? 

253, pp. 140- 142; 344, Chapter 
4, 5; 4 12, p. 498; 428; 459; 460; 
463 through 465. 

heat loss 


Wrapping steam pipes 

Exposed steam pipes are often 
covered with asbestos to minimize 
heat loss, and so we might conclude 
that asbestos is a poorer conductor 
of heat than the room air. Other- 
wise why would anyone pay for 
asbestos insulation? But, as a mat- 
ter of fact, asbestos is a better 
heat conductor than air. Why then 
is it used to cover pipes, if that 
seems precisely the wrong thing to 

253, p. 74. 



Thunderstorm wind direction 

"You don't need a weather- 

To know which way the wind 

---Bob Dylan, 

Subterranean Homesick Blues* 

When a thunderstorm is a few miles 

away and coming toward you, does 

the wind blow toward or away from 

the storm? Most likely you'll find 
that it changes direction as the 
storm gets closer. Why should it 
do that? 

300, p. 4; 362, p. 47; 363, pp. 

*© 1965 M. Witmark & Sons, all rights 
reserved. Used by permission of Warner 
Bros. Music. 



Insect plumes over trees 

There have been many observa- 
tions of dark plumes forming 
over tree tops near sunset (Figure 
3.88). Though the plumes look 
like smoke, closer inspection re- 



Silvery waves from your finger 

Sprinkle a small amount of 
aluminum powder into a squat 
jar of wood alcohol, screw on the 
top and put the jar in the refrigera- 
tor. Once it has cooled, remove it, 
and place your finger against the 
side of the jar. Silvery waves form 
and quickly spread away from your 

finger (Figure 3.87). What gener- 
ates the waves? (The powder 
serves merely to make them 
visible.) What would happen if 
instead you pressed an ice cube 
to the jar's side while the jar and 
alcohol are at room temperature? 


Figure 3.8 7 

Waves spread from your finger across the alcohol. (From "The Amateur 
Scientist'' by C. L. Stong. Copyright © 1967 by Scientific American, 
Inc. All rights reserved.) 

68 The flying circus of physics 

Figure 3.88 

Insect plumes over trees. 
[After J. H. Wiersma, Science, 
152, 387 (April 15, 1966), 
Copyright 1966 by the American 
Association for the Advancement 
of Science).] 

veals they are actually thick 
swarms of insects, usually mos- 
quitos, that have gathered above 
the trees. The columns are ver- 
tical and well defined and may 
even suggest a small fire in the 
tree. They have also been seen 
over TV antennas and church 
steeples. In fact, there is even a 
story about a fire department 
rushing out to fight a church 
fire only to find that the plume 
above the steeple was insects and 
not smoke. Why are these in- 
sect plumes formed? 

473 through 480. 



Shrimp plumes and Ferris wheel 

Shallow water brine shrimp as- 
cending in large numbers also take 
on the appearance of a plume 
(Figure 3.89). These plumes, which 
may be as large as several cubic 
meters, are always found over 
stones on the bottom. What's more, 
they are never found over shady 
stones, but only over those stones 
that enjoy some sunlight. In spite 
of this, however, the shrimp plumes 
frequently lean away from the sun. 
The questions to be asked about 
this are obvious. Why do the 
shrimp ascend in such large con- 
centrations only over sunlit stones? 
If the sunlight is desirable, then 
why do the plumes frequently lean 
away from the sun? 

A shrimp in the plume is carried 
up to the surface of the water, 
where it separates itself from the 
plume and swims back to the 
bottom. Why are the shrimp then 
drawn back to the plume to con- 
tinue their Ferris wheel ride? 









\\*\ Shrimp 



phase change 

latent heat 

human heat transfer 


Heat stroke 

If you ever mowed the lawn in the 
middle of summer as I used to do 
in Texas, you've probably wonder- 
ed how your body stays as cool 
as it does. A significant amount 
of thermal energy is generated in- 
side your body, up to 1400 kcal 
per hour during heavy physical 
exercise, and if that heat is not 
disposed of somehow, your 
body temperature could rise as 
much as 30° F per hour. Of 
course, that would soon be fatal. 
How is the heat dissipated? Can 
you trace the path by which it is 

Mowing the lawn in the midday 
on a once-a-week basis was 
miserable, for I always got heat 
exhaustion, yet there are people 
who do this daily without ill ef- 
fects. Somehow the body be- 
comes accustomed to working 
in the heat. What exactly happens? 
The heat is generated at the same 
rate internally, so the dissipation 
mechanism must somehow change. 

High temperatures in Texas were 
usually bearable because the 
humidity was so low. Why is it so 
much more uncomfortable in places 
with high humidity? 

344 , pp. 57-59; 482. 

Heat fantasies and other cheap thrills of the night 69 





thermal radiation 



Cooling a coffee 

Suppose you have just made a hot 
cup of coffee, but you've still got 
5 minutes until class. If you want 
to bring your coffee to class as hot 
as possible, should you put the 
cream in now or just before class? 
When should you add the sugar? 
When should you stir it and for 
how long? If you don't want to 
stir it, should you leave the 
spoon in? Does it matter whether 
the spoon is plastic or metal? 
Would your answer be different 
if cream were black instead of 
white? Does your answer depend 
on the color of your cup? Make 
numbers for your arguments if 
you can. 

transport and 



Polaroid color development 

If you take a color Polaroid picture 
on a cold day, you must develop 
it in a metal plate previously warm- 
ed by your body. If you don't, 
the colors will be off balance, be- 
cause when the dyes are cold, they 
will not reach the positive in the 
proper amount of time. Why does 
the temperature affect the transit 
time of the dyes that way? 


latent heat 


Heat islands 

Why is the temperature in a city 
higher than that in the surrounding 
countryside by 5 or 10 degrees 
(Figure 3.93)? In addition to there 
being more heat producers in the 
city, how is the temperature dif- 
ference affected by a city's tall 
buildings, expanses of rock and con- 
crete, quick rain drainage and snow 
removal, dust concentrations, fre- 
quency of smog and fog, etc.? 
Meteorologists who map the tem- 

perature distribution of a city, 
whether large or small, find a 
"heat island" concentrated near 
the city's center. Temperatures 
are lower as one moves away 
from the heat island, toward the 
suburbs and countryside. One 
consequence of this is that spring- 
time blooming of flowers should 
begin sooner near the city's center. 

344, pp. 78-81; 483 through 493. 

Figure 3.93 

Heat island of a city. 

kinetic theory 

ideal gas law 


Total kinetic energy in a heated 

A stove will warm the air in a 
room. Will it also increase the 
air's total thermal energy? (The 
thermal energy is kinetic energy 

of the air molecules.) Well, the 
air's thermal energy certainly 
depends on its temperature, 
and since the air is being warmed, 
the total thermal energy will be 
increased. That sounds correct, 
but one discussion of this claims 
that the total energy will not 
change. How can that be? 

343 ', pp. 40-4 1; 494 through 

70 The flying circus of physics 


may ignite clothing, paper, 
dry wood, and other simi- 


Snowflake symmetry 


larly combustible materials 

Smudge pots in the orchard 

at distances up to 15 kilo- 

Why are snowflakes six-sided (hexa- 

meters, and present capabil- 

gons or six-pointed stars), and why 

Why does a fruit grower put 

ities make it necessary to 

are the six arms exactly alike? How 

smudge pots in his orchard over- 

scale this range upward 

does one arm know what its neigh- 

night when he fears a frost? 

by an order of magnitude. 

bors are doing as the snowflake 

Since the pots are placed so far 

The resulting fire storm 


apart, they surely can't provide 

would in many populated 

much heat to warm the fruit. 

areas "escalate" until 

388, pp. 449-453; 404; 499 

What's the point then? Does 

destruction of life and 

through 506. 

the grower ever use them during 
the day? 

OO^l O/^rt. A ~7 <f <f firs 

property would be virtual- 
ly total (219). 
But if you are more than several 

surface tension 


330, p. 398; 471 , p. 130. 

kilometers from the blast site there 

is sufficient time (up to 3 seconds) 


to fall behind an obstacle for pro- 

Two attractive Cheerios 


tection. First of all, how exactly 
does the blast cause fires several 
kilometers from ground zero? 

If two fresh Cheerios* are placed 
near each other while floating on 



Second, why does this fire danger 

milk, they will rapidly pull 

A warm blanket of snow 

come at such a relatively long 

together. What force causes that 

time after the explosion begins? 

attraction? Is it possible to get 

Why is there less danger of crop 

219, pp. 307-310. 

the Cheerios to repel each other 

damage on a sudden cold day if 

for a suitably chosen liquid on 

there is a good snow cover on the 

which they are floated? 


*An O-shaped breakfast cereal from 
General Mills, Inc. 

crystal genesis 

160, p. 183; 4 13, p. 205. 


Growing crystals 

Why does it take small particles, 
perhaps impurities, to start crys- 



Cultivating farmland 

Wien's law 

atmospheric transmission 

tals growing in a supersaturated 

Why are farmlands in semiarid 



regions frequently cultivated (the 

Fires from A-bombs 


top soil is plowed and broken up 

into a loose texture)? If a foot- 

Of the multiple dangers to 

print is left undisturbed in cultivat- 

life which nuclear explosions 

ed soil, the soil inside the footprint 

present, ... the resulting 

will become hard and dry. Why 

setting of innumerable fires 

is that? 

is perhaps the worst. A 

158, pp. 141-142. 

single one-megaton bomb 

Heat fantasies and other cheap thrills of the night 7 1 

surface tension 



Wall curvatures of a liquid surface 

Some liquids have surfaces that 
turn up near a glass wall; others 
turn down. Why do they do this? 
What force pulls them up or 
down? What is the fundamental 
difference (on a microscopic or 
atomic scale) between those 
that slope up and those that slope 
down? Can you calculate what 
surface shape is expected? 

Some liquid drops will remain 
drops after being placed on a flat 
glass surface. What prevents them 
from spreading out? What is the 
fundamental difference between 
such a nonwetting liquid and a 
wetting one? Finally, what is the 
nonwetting drop's shape when it 
is sitting on the surface? 

Suppose a nonwetting liquid is 

Figure 3.102 

Which way does the nonwetting 

liquid curve? 

in a small trough as shown in 
Figure 3.102. Which shape do 
you expect? Or is either pos- 
sible, depending on the trough's 
angle? If the latter, at what angle 
is the liquid flat? 

51, pp. 127- 128; 32 1; 507 
through 511. 

osmotic pressure 

atmospheric pressure 

negative pressure 


Rising sap in trees 

How does sap rise in trees, especial- 
ly in very tall ones (some redwoods 
are 360 feet high)? Certainly there 
is a pressure difference between 
crown and roots, but why? Does 
the tree act like a suction pump? 
If so, then shouldn't all tree 
heights be limited to 33 feet since 
that is supposedly the maximum 
height of a suction pump? Some 
other mechanism must be involved. 

512 through 519. 

osmotic pressure 




Ice columns growing in ground 

Have you ever seen columns of 
ice growing out of the ground, 
perhaps about IV2 inches high? 
Upon close inspection you may 
find bits of soil and pebbles on 

top of the columns. Strangely 
enough, when the columns form, 
the ground itself is unfrozen and 
usually wet. What makes these 
columns grow? If the temperature 
is low enough to cause freezing, 
shouldn't there be ice on the 
ground? Finally, what will limit 
a column's height? 

338, p. 133; 521. 


osmotic pressure 

freezing water 


Crowing stones in the garden 

If you have ever taken care of a 
garden, you may be aware of the 
annual crop of stones that must he 
cleared from the garden each spring. 
Though some regions don't have 
this problem, others, New England 
for example, have an abundant 
stone crop. Robert Frost's 
"Mending Wall" is about such a 
crop of stones. 

The stones obviously migrate up- 
ward from the rock bed below the 
soil, but why? The stones, after 
all, are denser than soil and should 
gradually move down, not up. 
What's forcing those stones up? 
A simple simulation of this stone 
migration, suitable for the class- 
room lab, is given in Bowley and 
Burghardt (522). 

403; 522 through 526. 

72 The flying circus of physics 

osmotic pressure 

capillary and 


osmotic forces 



Winter buckling of roads 

"Something there is that 

doesn't love a wall, 

That sends the frozen -ground- 
swell under it 

And spills the upper boulders 

in the sun" 

---Robert Frost, "Mending 

If you have ever lived in the north 
you might have seen pavement 
develop bumps (on blacktops) 
or cracks (in concrete) or even 
become tilted during the winter 
(Figure 3.106). These bumps 
can sometimes be as high as a 
foot. What could cause this? 
My first guess would be that 
water underneath the pavement 

expanded in freezing, but it 
would require so much water 
to make these large bumps 
that such an explanation is 
hard to accept. So, what does 
cause the bumps? 

338, pp. 131-133; 403; 520. 

*From "Mending Wall" from The 
Poetry of Robert Frost edited by 
Edward Connery Lathem. Copyright 
1930, 1939, © 1969 by Holt, Rinehart 
and Winston, Inc. Copyright © 1958 
by Robert Frost. Copyright © 1967 by 
Lesley Frost Ballantine. Reprinted by 
permission of Holt, Rinehart and 
Winston, Inc., the Estate of Robert 
Frost, and Jonathan Cape Limited. 

Figure 3.106 

Buckling of road in the winter. 


Shorting out a masonry wall 

Masonry walls usually become 
damp, especially near the ground. 
One way to prevent this is to 
ground the wall electrically by 
running a wire from the wall to 
a metal stake in the ground 
(Figure 3.107). No batteries or 
other such power source are 


Figure 3.107 

Drying a masonry wall by 

electrically grounding it. 

used, only a simple metal stake 
and wire. How would shorting 
out the wall in this way prevent 
moisture in the wall? 


surface tension 


Soap bubbles 

What keeps a soap bubble together? 
Is it really spherical? What is the 
pressure inside the bubble? Does 
a bubble go up or down in air? 

Heat fantasies and other cheap thrills of the night 73 

Is there any part of the surface 
that is most likely to burst first? 

322; 528 through 532; 533 f 
pp. 139 ff. 

surface tension 



Inverted soap bubbles 

Inverted soap bubbles— where the 
water and air have traded places- 
can easily be made by carefully 
pouring soapy water into a dish of 
water from a height of a few 
millimeters. If you pour slowly, 
drops skim across the water surface. 
If you pour a bit faster, a drop may 
penetrate the water and remain 
there with a shell of air trapped 
around it, thus forming an inverse 
soap bubble (Figure 3.109). 

Will these soap bubbles show 
colors as normal ones do? Will they 
have uniformly thick shells? Will 
the bubbles go up or down in the 
water dish? Finally, do you think 
there will be continuous evapora- 
tion from the inner drop into the 
air shell, eventually leading to. a 

534; 1608. 

Figure 3.109 



A candle's flickering death 

Why do many candles, especially 
small ones, flicker and pop in the 
last moments before burning out? 
What determines the frequency of 
the flickering? 




Dust explosion 

One of my most delightful under- 
graduate tricks was to replace a 
friend's overhead light bulb with 
a short wire and a bag with some 
flour in it. The wire almost com- 
pleted the circuit so that there 
was a spark when the light 
switch was thrown. Just before 
the victim appeared, I shook the 
bag to fill it with floating flour 
dust. Got the picture? My 
friend turned on his light, there 
was a spark, and the dust exploded, 
neatly covering his entire room 
with a layer of flour. Such dust 
explosions are very serious prob- 
lems in some industries where 
static electricity builds up in a 
room full of dust. In either case, 
why does a spark cause an explo- 
sion of the floating dust? 

536 ', pp. 383-384; 537 through 


thermal conduction 

Figure 3.112 


Davy mine lamps 

The open flame miner's lamp is 
very dangerous if the miner en- 
counters explosive gases. The 
danger can be avoided, however, 
if a fine mesh screen is placed 
over the flame holder as shown 
in Figure 3.112. The screen cer- 
tainly can't prevent the explosive 
gas from reaching the flame, but it 
nevertheless prevents the explosion. 

110, p. 171; 155, p. 232; 41 3 f p. 
205; 54 1, pp. 74-75; 542. 

74 The flying circus of physics 



Mud polygons and drying cracks 

You have frequently seen cracks 
in dried mud, but have you ever 
wondered why the cracks form 
or tried to explain their polygonal 
appearance? Sometimes the edges 
of the polygon will curl up, per- 
haps even so far that a tube 
develops, separates from the sur- 
face, and rolls away. 

Ever since airplanes and aerial 
photography came into prom- 
inent use, giant polygons have been 
seen in the dry desert basin bottoms 
that have periodically had water. 
By giant I mean the widths 
of the polygons can be up to 300 
meters and a fresh fissure may be 
as much as a meter wide and five 
meters deep. 

Why do the cracks and tubes 
form? If the ground cracks into 
polygons, is there any reason to 
believe, as some authors have 
argued,, that the polygons tend to 
be pentagons or hexagons? In other 
words, is there any preferential 
angle at which two cracks will 

543 through 551. 



Thermal ground cracks 

Mud cracks are not the only type 
of patterned ground you can find. 
For example, polygonal cracks are 
found in the permanently frozen 
ground of the arctic and subarctic 
regions. What causes the cracking 
in this case? Is there any pre- 
ferred angle between cracks at 

438; 552 through 556. 


colloidal suspension 


Stone nets 

As a final example of patterns in 
the ground, stone nets-circles 
and polygons of sorted stones 
(Figure 3.1 15)-should be men- 
tioned. What brings the stones 
from a random distribution into 
such geometric shapes? 

556 through 558. 

o ... 





■<0i'.': :: ". ."■&.'■:" ..'■'■■-. '.' 9 -V. 

Figure 3.115 

Naturally occurring circles of 



Figure 3.116 

"Now, in the second law of 

thermodynamics.. " 



Life and the Second Law 

"As you stay in a given 
place, things and people 
go to pieces around you." 
- ■ -Celine 
In thermodynamics one learns that 
entropy, which is a measure of 
disorder in a system, always in- 
creases in an irreversible process 
(the so-called Second Law of 
Thermodynamics). What about 
birth and life? Isn't the creation 
and growth of a human being a 
violation of this rule, for in that 
process, doesn't order increase? 
Isn't the rule also violated by 
the evolution of all animals over 
millions of years?* 

559 through 562. 


*A similar problem, whether or not 
quantum mechanics can explain life, is 
covered in Mehra (1569). 

Heat fantasies and other cheap thrills of the night 75 

The madness 
of stirring tea 


(4.1 through 4.14) 

fluid pressure buoyancy 

Pascal's law 

Archimedes' law 


Holding back the North Sea 

Remember the story of the Dutch 
boy who saved his town by 
thrusting his finger into a hole he 
discovered in the dike? How did 
he do it? How could one little 
boy hold against the pressure 
of the whole North Sea? 

418, p. 68. 


Breathing through air tube 

To what depth can you breathe 
through a simple air tube while 
swimming under water? What 
determines the limiting depth? 



Measuring blood pressure 

Why do doctors always measure 
blood pressure on your arm at a 
height about even with the heart? 
Couldn't they just as well measure 
it on the leg? 

4 12, p. 191. 

Exceptionally good references: Craw- 
ford's Waves ( 1 70) is the best example 
of real -world physics in a major text- 
book I have found. See also Tricker 
(399), Scorer (364), Lodge (923), and 
Schaefer (830). 


Last lock in Panama 

A ship is waiting patiently in the 
last lock of the Panama Canal as 
the water level is lowered. When 
enough drainage has taken place, 
the gate begins to swing open 
toward the ocean, and the lock 
director engages the machinery to 
finish opening it. The ship then 
begins to move out to sea with- 
out the aid of a tugboat and with- 
out using its own power. What 
forces it seaward? 



Panama Canal ocean levels 

You may already know about the 
difference in ocean levels at the 
two ends of the Panama Canal. 
During the dry season the dif- 
ference is small, but during the 
rainy season it can be as much 
as 30 centimeters. Why aren't 
the ocean levels the same? 



Hourglass's bouyancy 

If an hourglass is floating in a 
narrow tube of water as shown in 
Figure 4.6, will it float again if 
the tube is inverted? The sand that 
was initially in the lower part of 
the hourglass is now pouring down 
from the upper part. The weight 
and volume of the hourglass are 
the same, however, so the hourglass 

I I 



I I 

] [ 

Figure 4. 6 

When the tube of water is turned 
over, why doesn't the hourglass 
float up? (From "Mathematical 
Games'' by Martin Gardner. 
Copyright © 1966 by Scientific 
American, Inc. All rights reserved.) 

should float back up to the top. 
Instead, it stays at the bottom of 
the tube until the sand has 
poured into the lower section. 
Why? Does the buoyancy of the 
hourglass really depend on whether 
the sand is in the lower or upper 



Boat sinking in pool 

There is a famous problem about 
throwing a stone from a boat into 
the swimming pool where the 

The madness of stirring tea 77 

boat is floating. When the stone 
is thrown from the boat, does the 
water level rise, fall, or remain 
unchanged? This problem was 
asked of George Camow, Robert 
Oppenheimer, and Felix Bloch, 
all excellent physicists, and to 
their embarrassment, they all 
answered incorrectly. 

What happens to the water 
level if a hole is made in the 
bottom of the boat and the boat 
sinks? If the water level changes, 
when does the change begin? In 
particular, does it begin to change 
when water first enters the boat? 



Coiled water hose 

If you try to pour water into a 
coiled hose, as shown in Figure 
4.8, no water will come out the 

Figure 4.8 

(From ^Mathematical Games'' 
by Martin Gardner. Copyright 
© 1966 by Scientific American, 
Inc. All rights reserved.) 

other end. Indeed, surprisingly 
little water will even enter the 
hose. Why? 



C _ J .„. 


mi A 

r n.. 





^ M " 


mi A 

r in. 



Bh§E = 

: = 2 




Figure 4.9 

[After L. E. Dodd, Amer. J. Phys., 

23, 113 (1955).] 


Floating ship in dry dock 

When a ship is put into dry dock, 
the water is removed as the dock 
is made smaller (Figure 4.9). What 
is the minimum depth of water 
under, say, a two-ton ship that 
will still support the ship? 

567; 568. 


Submarine stability 

How does a submarine ascend 
and descend? How does it re- 
main submerged at a fixed depth? 
Shouldn't changes in the water 
density at the submarine's depth 
make the submarine unstable? 
Sure, small corrections for the 
changes could be made, but 
such corrections are impractical. 
Besides, if quiet conditions are 
essential to avoid detection, then 
constant corrections are certainly 

Fortunately, there are many 
depths in the sea where a sub- 
marine is stable against the sea's 
perturbations. What is peculiar 
about those regions, which are 
called thermoclines? 



Floating bar orientation 

Does a long, square bar float on a 
side or tilted over on an edge 
(Figure 4.11)? Even if you find 
the answer obvious, try floating 
several long square bars in a variety 
of liquids and then classify your 
results according to the relative 
density of the bar and liquid. 
Is your intuition correct? 


Figure 4.11 

78 The flying circus of physics 


Fish ascent, descent 

Do fish ascend and descend the 
same way as submarines? Do they 
compress and expand their swim 
bladder to change depth? This may 
be a common explanation, but it 
isn't correct because a fish has no 
muscular control over its swim 
bladder. So how do they do it? 

Although fish can't survive rapid 
depth changes (in trawling, cod 
and hake are dead when pulled to 
the surface because of this), they 
can live at tremendous depths. 
For example, fish at 15,000 feet 
withstand a pressure of 7000 
pounds per square in ch . Wha t 
provides the resistance to such pres- 


air pressure 

surface tension 


Inverted water glass 

Place a piece of cardboard over 
the mouth of a glass of water. 
(The glass does not have to be full.) 
Invert the glass, holding the card- 
board in place. Now remove your 
hand from the cardboard— it 
stays in place and, therefore, the 
water stays in the glass. Why? 

Try the same thing with a long 
glass tube (about 60 centimeters 
long and 3 or 4 centimeters in 
diameter) that is sealed at one 

end. Whether the inverted ar- 
rangement is stable or not depends 
on how much water is in the tube 
but probably not in any way you 
would have guessed. If the tube 
is nearly full or nearly empty, it is 
stable when inverted with the 
cardboard. But if it is about half 
full, the water falls out every time. 



Floating bodies 

Why do drowning victims first 
sink and then, after a few 
days, float to the surface? 

gravity waves 

Rayleigh-Taylor instability 


Stability of an inverted glass of 

If the cardboard used in Problem 
4.13 were to disappear suddenly 
with the water glass inverted, why 
would the water fall out? Yes, I 
know gravity will pull the water 
down, but how does the falling 
start? Isn't the water surface ini- 
tially stable? Isn't it precisely the 
same forces holding it up against 
gravity? Once you decide why the 
falling begins, can you figure out 
how long it will take to empty 
the glass? 

574 through 579. 



molecular and thermal diffusion 


The perpetual salt fountain 

Tropical and subtropical oceans 
have warm, salty water near the 
surface and cooler, less salty 
water below. A seemingly perpe- 
tual fountain may be made by 
dropping a tube to the bottom, 
and pumping water to the surface. 
The pump can then be removed, 
and the fountain will continue 
itself (Figure 4.16). What keeps 
the fountain going? Is it truly 

580, pp. 44-45; 581; 582; 1546. 

Figure 4.16 

Perpetual salt fountain in the 


The madness of stirring tea 79 




nonlinear system 

molecular and thermal diffusion 

Rayleigh instability 


Salt fingers 

You can see a phenomenon related 
to the salt fountain in your 
kitchen by half filling an aquarium 
with cold, fresh water and then 
adding (carefully, without mixing) 
a solution of warm, dyed salt 
water on top. (The dye is only 
meant to be a tracer.) Immediate- 
ly fingers of the upper solution 
extend into the underlying fresh 
water, making the boundary area 
translucent (Figure 4.17). You 
can see the fingers without the 
temperature difference if you 
pour a sugar water solution over 
a salt water solution. (Again, use 
a dye for a tracer.) What initiates 
the finger growth, and why are 
the fingers so stable? 

582 through 590. 



Figure 4.17 

Salt fingers (exaggerated scale). 

HH? Dyed £-3? 
^H? salt watery: 

I-I 1 ! 1 : 1 ! 1 !^ 

::: ::^ 


- -^ FrPQh water - 


-_-_-_-_-_-_—- -_-_-_-_-_-_-_-_-_" 

Figure 4.18 


Salt oscillator 

If you take an ordinary tin can, 
punch a pinhole in the bottom, fill 
it with saturated salt water, and 
partially immerse it in a container 
of fresh water, will the two solutions 
eventually mix? Well, yes, they 
will, but in a surprising way. (Color 
one of the solutions with a dye so 
you can see which is which.) There 
will be an alternating exchange of 
solutions, that is, salt water will 

flow down through the hole, then 
fresh water will flow up, and so on 
(Figure 4.18). This oscillation 
may continue for as long as four 
days, with an oscillation period 
of about four seconds. Why is 
there such an oscillatory exchange 
of fluid, and what determines the 


Bernoulli Effect 

(4.19 through 4.40) 


Narrowing of falling water stream 

Why does a smoothly flowing 
stream of water from your faucet 
narrow as it falls? Is there some 
force squeezing it together? Can 
you calculate the change in the 
stream's diameter as a function of 
the distance from the faucet? 


Beachball in an air stream 

To catch the attention of cus- 
tomers, vacuum cleaner salesmen 
will sometimes reverse the air flow 
in a cleaner and then balance a 
beach ball in the exhaust jet (Figure 
4.20). The ball is quite stable 
and can be held in place with 
the air jet at a considerable angle. 
Even a good slap will not be 
enough to release it from the 
jet. Why is it so stable? Will the 

80 The flying circus of physics 


Figure 4.20 

ball spin in any particular direc- 

211, p. 155; 399, pp. 102-103; 
592, p. 60; 593. 


Toy with suspended ball 

A toy, "a-Blow-Go"*, uses this 
suspension trick also. You 
balance a light ball by blowing 
through a small side tube, as 
shown in Figure 4.21. With a 
long, hard blow, the ball is lifted 
until it is pulled into the top of the 
tube and shot back to its original 
position. The point of the game 
is to circulate the ball this way 
as many times as possible within 
one breath. (My record is five 

Blow in 

Figure 4.21 

By blowing through the side 
tube, you make the ball circulate 
through the main tube. 

complete circuits.) What makes 
the suspended ball stable, and what 
makes the ball enter the top tube? 

Norstar Corp., Bronx, New York 

momentum transfer 



Figure 4.22 

Ball suspended in water jet 


Ball balanced on a water jet 

In another similar trick, a ball is 
balanced on a vertical water jet 
(Figure 4.22). Occasionally the 
ball may sit still for several seconds, 
but usually it wavers and bobs. 
Why doesn't the wavering cause it 
to fly out of the jet? What holds 
it in? Does this really involve the 
same physics as the beach ball 

To be honest, the ball does some- 
times escape the jet, but in the 
course of its fall, it reenters the jet 
and is returned to its former posi- 
tion. It will even do this in a 

vacuum. What entices the ball back 
into the stream like this?* 


*For yet another suspension but with 
photons instead of air or water, see 
Prob. 5.104. 


Egg pulled up by water 

Let a faucet pour onto an egg 
floating in a glass of water (Figure 
4.23). For flow rates above some 
critical value, the egg will rise as 
if it were attracted to the falling 
water. Why, and what determines 
the critical flow rate? 

Figure 4.23 

Egg pulled upward by water stream. 

The madness of stirring tea 8 1 

momentum transfer 



Spoon in a faucet stream 

If you hold a light spoon round 
side upward in a stream of water 
as shown in Figure 4.24, the spoon 
seems to be glued to the stream. 
You can move your fingers several 
inches away, putting the spoon 
at a considerable angle, and the 
spoon will still refuse to leave 
the stream. The falling water 
should, by all rights, push the 
spoon away, not attract it. What 
causes this? 

592, p. 60; 595; 596. 

Figure 4.24 

The spoon is kept in place by the 

water stream. 


Water tube spray guns 

If you put one end of a tube into 
water and blow across the open end 
(Figure 4.25), you can force water 
up the tube. With a strong blow 

Figure 4.25 

Water is lifted up the tube by the 

air blown across the tube. 

across a short tube, you can soak 
your friends. The aerosol can is a 
more practical application: pres- 
surized air blows across a narrow 
container of the material to be 
sprayed. How do such spray 
guns and cans work? 



Passing trains 

When high-speed trains pass each 
other, they must slow down or 
their windows will be broken. 
Why? Will the windows be pushed 
into the train or sucked out? Will 
this happen if the trains are travel- 
ing in the same direction? If you 
stand near a high-speed train, will 

you be pulled toward or pushed 
away from the tracks ... or both? 

599 through 602. 


Ventilator tops and prairie dog 

Why is the draft through a ventila- 
tor pipe improved if the top of the 
pipe is surrounded with a cone 
(Figure 4.27a)? Similarly, why is 

Figure 4.27a 

Ventilator pipe with cone top. 

the ventilation inside a prairie dog 
tunnel improved if the entrances are 
surrounded by high, conical mounds 
(Figure 4.27b)? 

139, pp. 179-180; 598. 

Figure 4.27b 

Prairie dog hole with high 


82 The flying circus of physics 



Insects rupturing on windshields 

Are insects squashed directly on 
the windshield of fast moving cars, 
or do they rupture in the air and 
then splatter on the windshield? 
If the latter is the case, then what 

causes the rupture? You may be 
tempted to blame the insect's 
fate on turbulence, but is there 
really that much turbulence? Why 
doesn't the strong, deflected wind 

stream carry the bugs safely over 
the car? (Figure 4.28 shows one 
way to avoid the bugs.) 

364, pp. 12-13. 


Do Voo \^ANr Wis 
with <9r without , 
the &0& screen p 

Figure 4.28 

(By permission of John Hart Field Enterprises.) 

eddy formation 


Flapping flags 

Why does wind, even a uniform 
wind, make flags flap? What 
determines the frequency of the 

124, p. 115; 453, p. 51. 

Bernoulli effect 

momentum transfer 


Wings and fans on racing cars 

Racing cars have gone through a 
great many changes over the years, 
some obvious, some subtle. One 
of the best developments was the 

addition of a horizontal wing above 
the rear of the car. When a car 
with such a wing entered a curve, 
the driver would tilt the wing for- 
ward. Upon leaving the curve, the 
wing was leveled again. This wing 
and its adjustments proved very 
useful in keeping a car on the road 
in turns, hence allowing much 
higher speeds there. Were it not 
for the danger of broken wings 
resulting in uncontrollable cars 
on the tracks, these movable wings 
would still be in use. But safety 
forced the racers to fix their wings 
in place. In either case, movable 
or fixed wing, how would a wing 
help in keeping the car on the 

One of the strangest versions of 
a racing car has been the Chaparral 
2J, which was built by Jim Hall 
who also pioneered the movable 

wing. The Chaparral 2J had two 
large fans in its rear designed to 
pull air beneath the car, through 
the fans, and out the rear. Skirts 
were built along the bottom sides 
of the car, hugging the road, so as 
to tunnel the air beneath the car. 
Again, Hall greatly increased the 
speed of his cars by increasing 
the traction. But how? Why would 
air tunneled beneath the car and 
out the rear increase traction? 
Can you estimate the resulting in- 
crease in traction and speed? 


The madness of stirring tea 83 

Bernoulli effect 

momentum transfer 


Lifting an airplane 
"How does an airplane gain lift?" 
is a standard physics question, 
and the standard answer involves 
Bernoulli's principle, but is that 
the only, or even the major, 
factor? If the wings are shaped 
(as is in Figure 4.31) to produce 
a Bernoulli effect, then how do 
airplanes fly upside down? 

The crucial point of the standard 
argument is that the air moves 
faster over the wing than under 
the wing, and this means, because 
of Bernoulli's principle, there 
is greater air pressure beneath the 
wing. Hence there is lift. Why 
does the air move faster over 
the top? Well, the two streams 
of air moving below and above the 
wing must cross the wing in the 
same amount of time. The air 
moving above has a greater dis- 
tance to travel and thus moves 
faster. Here the standard argument 
stops. But why must the upper air 
traverse the wing in the same time 
as the lower air? This is rarely 
explained. As a matter of fact, 
the top and bottom streams have 
unequal traversal times. So, 
why does the wing have lift? 
593; 603 through 605. 

Figure 4.31 

Cross section of airplane wing. 


Pulling out of nose dive 

Suppose a plane stalls and goes into 
a nose dive. Why must the pilot 
wait until he reaches a high speed, 
higher than his normal cruising 
speed, before he attempts to pull 
out of the dive? 



Sailing into the wind 

It's not difficult to see how a sailing 
boat can be pushed along with the 
wind, or at some angle to it, as 
long as that angle is not too large. 
But not only can sail boats travel 
90° to the wind, they can even 
sail into the wind at an angle of 
45° or more. In this case the 
wind will obviously oppose the 
motion of the boat, right? So what 
does push the boat when it sails 
windward? Disregarding water 
currents, what angle will give 
the fastest boat speed? 

611 through 613. 



What keeps a Frisbee* aloft? Must 
it be spinning? It apparently 
doesn't have to be a disc, because 
Frisbee rings work almost as well. 

*® Wham-0 Manufacturing Company, 
San Gabriel, California. 

84 The flying circus of physics 


Manpowered flight 

Is it possible for a man to fly under 
his own power (Figure 4.35)? The 
question is an old one but far from 
dead. It now seems that present 
attempts to design manpowered 
aircraft will eventually lead to a 
working model. 

Some of the problems in design- 
ing the aircraft are how much 
power can a man produce, and 
how much is needed for flight? 
How large should the wings be? 
Should they flap? Is the lift 
improved if you stay close to 
the ground? 

606 through 610; 1518; 1519. 

Figure 4.35 

Man in glorious flight 

Figure 4.36 

Top spin on golf ball causes it to roll forward. 


Golf ball top spin 

To gain distance, some golfers will is this really a wise thing to do? 

give a top spin to their ball so that 
it will roll farther after it has hit 
the ground (Figure 4.36). Con- 
sidering the ball's total trajectory, 

36, pp. 53, 138- 139; 399, pp. 
103-104; 593; 616 through 
621; 1484. 


Flettner's strange ship 

In 1925 a most unusual ship crossed cylinder to an airplane's wing, 
the Atlantic propelled by two large, How would such a cylinder pro- 
vertical rotating cylinders (Figure vide lift for the airplane? 

4.37). How did those rotating cyl- 
inders drive the ship forward? 

In a more modern application, 
NASA has used the same principle 
by adding a horizontal rotating 

/ 10, p. 22; 155, p. 1 17; 399, 
p. 105; 453, pp. 71-72; 615; 

Figure 4.37 

Flettner's ship propelled by two rotating cylinders. 

The madness of stirring tea 85 

Figure 4.38 

Strong winds through building. 


Winds through a building 

In one type of modern building 
design, the floors are hung like 
bridges between two solid walls 
and the ground level area is left 
open (Figure 4.38). This is an at- 
tractive design, but inconvenient in 
windy regions. For example, when 
the spring winds blew through one 
such building at MIT, wind speeds 
up to 1 00 miles per hour were 
measured, certainly much higher 
than elsewhere on the campus. 
(Students and junior faculty alike 
were bowled over by the wind; 
only full professors could with- 
stand the gale.) What causes this 
enhancement of wind speed? 



Curve, drop, and knuckle balls 

Can baseball pitchers really throw 
curve balls, drop balls, and knuckle 
balls? If they can, then explain 
how each is thrown. Does a curve 
ball break continuously or sud- 
denly? Does a drop ball suddenly 
drop? And does a knuckle ball 
actually dance, as batters claim? 
How far will a major league 
pitcher's curve ball deviate from a 
straight line by the time it 
crosses home plate? 

36, pp. 53, 138- 139; 211, p. 
156; 593; 615 through 622. 


Curves with smooth balls 

A smooth ball should not curve 
since, unlike a baseball, it has no 
rough surface with which to "grab" 
the air. You can nonetheless throw 
a curve with a smooth ball, but it 
will curve in precisely the opposite 
direction as will a baseball. Why? 

593; 619 through 622. 


(4.41 through 4.59) 

wave speed (group and phase) 

superposition refraction 

interference dispersion 


Bernoulli effect 

flow around obstacle 

driven oscillator 


Building waves 

How are periodic water waves 
built up by random gusts of wind 
that play along a water surface? 
Is the wind drag across the surface 
more important than vertical dis- 
turbances? Is there a minimum 
wind speed required to maintain 
the water waves? Do the waves 
provide a feedback to the wind 
flow to build up the waves even 

399, pp. 141-147; 580, pp. 133- 
136; 624; 625. 

wave interference 


Monster ocean waves 

There are many stories about ships 
at sea suddenly encountering in- 
credibly large waves. For example, 
a wave 100 feet high was seen by a 
cargo vessel captain in 1956 off 
Cape Hatter as, and there were 
reports of 80 foot waves in the 
North Pacific in 1 921 . In 1 933 a 

86 The flying circus of physics 

wave estimated at 112 feet high 
was seen by the U.S.S. Ramapo 
in the North Pacific. Imagine 
standing on the bridge beneath a 
wave 112 feet high! 

Why do these waves suddenly ap- 
pear and then disappear? If they 
are somehow caused by storms, 
then shouldn't there be more than 
one large wave? Could they be 
caused by a sudden underwater 
earthquake? (Can such earth- 
quake waves be detected by a ship 
at sea?) 

399, p. 138; 626, pp. 48-49; 
627; 628; 629, pp. 53-60. 

wave velocities 

light scattering 



Why exactly do whitecaps form on 
the ocean and other bodies of water, 
and why are they white? In a 
moderate wind, why do they often 
appear in succession, each forming 
down wave of the previous one with 
a time interval of a few seconds 
between appearances? 

390; 630; 631. 

gravity and capillary waves 


Whirligig beetle waves 

When a whirligig beetle skims 
quickly along the surface of the 
water, why does it make pro- 
nounced waves in front of itself, 
but in back barely visible waves 
or none at all (Figure 4.45a)? 
If it skims slowly, there are no 
waves, front or back. Why? A 
boat doesn't do this; it always 
makes waves to the rear. What is 
so different about a skimming 
water beetle? 

Figure 4.45a 
Whirligig beetle waves. 

A similar asymmetry is present 
in the wave pattern around a 
narrow obstacle in a moving 
stream: the waves upstream have 
a much smaller wavelength than 
those downstream (Figure 4.45b). 
What causes the asymmetry, and 
what determines the wavelengths 
in the two cases? 

633; 634. 

Figure 4.45b 

Waves around stick in moving 

stream. [Both figures after V. A. 

Tucker, Physics Teacher, 9, 10 



Bernoulli effect 


Boat speed and hydroplaning 

What determines the practical 
speed limit of boats, ducks, and 

other things larger than insects? 
If the limitation is friction from 
the water, then why does a 
longer boat generally have a 
higher maximum speed? Wouldn't 
a longer boat feel more friction 
and hence have a lower maximum 

Why can a hydroplane go much 
faster than a normal boat of similar 
length? It is, as you know, partially 
lifted out of the water. How is the 
lifting accomplished, and how does 
it permit such high speeds? 

6 32; 633. 

The madness of stirring tea 87 


nonlinear wave 



Figure 4.46 

Ship waves as seen from above. [After H. D. Keith, Am. J. 

Phys., 25, 466 (1957)]. 


Ship waves 

If you ever have a chance to fly 
over ships moving in deep water, 
examine their wave patterns. 
Notice the disturbed areas are 
always V-shaped with the same 
angle (38° 56'). As one writer 
put it, the V shape is present 
"whether the moving object is a 
duck or a battleship" (760). 
Why is that? 

Inside the disturbed area, the 
pattern gets more complicated 
(Figure 4.46). Can you explain the 

origin of the two types of wave 
crests that are present? Are they 
also the same for a duck and a 

How does the pattern change in 
shallow water? First, can you ex- 
plain what "shallow" means? Shal- 
low compared to what? 

51, pp. 200-203; 399, Chapter 
17; 635, Chapter 8; 636 
through 640. 


Edge waves 

While investigating water waves, 
Faraday discovered a very curious 
form of wave produced by a simple, 
horizontally oscillating plate 
slightly immersed in a water basin 
(Figure 4.47a). Ignoring wave re- 
flections from the basin's sides, 
I would have guessed that only com- 
mon, plane waves would be made. 
However, when the oscillating 
plate was immersed about 1/6 inch, 
he saw the following: 
Elevations, waves or crispa- 
tions immediately formed 
but of a peculiar character. 
Those passing from the sur- 
face of the plate over the 
water to the sides of the 
basin were hardly [visible] , 
but apparently permanent 
elevations formed, begin- 
ning at the plate and pro- 
jecting directly out from 
it to the extent of 1/3 or 

Figure 4.47a 

Plate oscillating in water. 

88 The flying circus of physics 

Figure 4.47b 

Edge waves on the oscillating 

plate, as seen from above. 

1/2 an inch or more, like 

the teeth of a very short 

coarse comb [Figure 

4.47 6] (643). 
Faraday also noticed these 
strange waves had half the fre- 
quency of the vibrating plate. 
Now how can a vibrating plate 
possibly set up standing waves 
whose crests are perpendicular 
to the plate?* 

64 1 through 646. 

*To see the edge-wave theory used to 
discuss rip currents on ocean beaches, 
see Rets. 647 through 651 and Ref. 



Swing of waves to shore 

When ocean waves reach the shore, 
why are they approximately parallel 
to the shoreline? Surely the waves 
originally come from a variety of 

360, p. 28; 399, pp. 95-96; 628; 
635, pp. 133-136. 

shallow water waves 

Bernoulli effect 


Surf skimmer 

You can surf, in a sense, on 
water only one or two inches deep 
by riding a wooden disc skimming 
along the shallow surf (Figure 
4.49). If you leap on it when it 
has sufficient speed, you may be 
carried 20 feet or more. What 
holds you up during such a ride, 
and why does this support disap- 
pear when the disc slows down? 
Why do longer boards travel 
farther? Shouldn't a longer 
board provide more friction and 
hence stop sooner? 

626 f pp. 152-156; 653. 


Figure 4.49 

shallow water waves 

wave speed 



What rushes you to shore when 
you're surfing? Are you pushed 
by the wave, or are you continously 
falling downhill? Why are the 
best waves to ride those on the 
verge of breaking, and why is 
most surfing done in waters over 
gently sloping beaches? Why is 
the surfing position on the wave 
front relatively stable? Is a 
surfer more stable on a long board 
than on a short board? 

626; 652 f pp. 80-81. 




Bow-riding porpoises 

Porpoises are often seen riding 
motionlessly a few feet beneath 
the water surface near a ship how. 
They make no swimming motions 
at all, so they somehow gain their 
propulsion from the ship itself. 
The technique must be well 
developed, for a porpoise can ride 
for more than an hour with little 
or no effort and can remain sta- 
tionary, flip over on a side, or 
even slowly revolve around its body 
axis. There may even be two or 
three layers of the porpoises, all 

The madness of stirring tea 89 

bow riding together. What actually 
carries the porpoises along? 
A similar case is related by 
Jacques Cousteau in one of his 
underwater books (660). Sharks 
are often accompanied by small 
"pilot fish" that, according to 
legend, guide the shark. Cousteau 
saw one such pilot fish, a very 
small one, directly in front of 
the shark's head, somehow being 
propelled along by the shark it- 
self. That was a precarious posi- 
tion indeed! How was the pilot 
fish pushed, and why was his 
position so stable? 

654 through 660. 


noninertial forces 

static and harmonic 
theories of tides 


Ocean tides 

What causes the ocean tides? You 
may be satisfied in answering that 
the tides are driven by the gravita- 
tional attraction of the moon and 
sun, but let me ask a few more 

Does the water bulge on the 
moon side of the earth because 
the moon pulls the water vertically 
away from the earth? If it does, 
that seems strange because 
isn't the water's attraction for the 
earth much, much greater than its 
attraction for the moon? 

If the earth's seas are pulled 
to the moon and the resulting 
bulge in the ocean is the high tide, 

To moon 

Figure 4.52 

Two tides on the earth 

(exaggerated, of course). 

then why are there two high tides 
a day? The earth turns once a day, 
and hence each point on the earth's 
surface should face the moon only 
once a day. Therefore, shouldn't 
there be just one high tide a day? 
However, since there are two high 
tides a day, the water on the 
earth should have two bulges, one 
of them being away from the 
moon (Figure 4.52). How do you 
explain the second bulge? 

Some seas, (the South China 
Sea, the Persian Gulf, the Gulf of 
Mexico, and the Gulf of Thailand, 
for example) have only one high 
tide a day. Why don't they have 
two? Still other places, such as 
the Indian Ocean, have alternating 
diurnal and semidiurnal tides. 
Again, why? 

Finally, why isn't there a high 
tide when the moon is directly 
overhead? For some reason, there 
is always a lag. 

/ 1 1; 399, pp. 3-14; 661, Chapter 
5, pp. 149- 181; 662, pp. 26-32, 
40 ff; 663, Chapter 4, pp. 1 1-55; 
664, pp. 177, 179, 188 ff; 665, 
pp. 195 ff; 667 through 669; 


Tides: sun versus moon 

Which provides the stronger 
driving force on the tides, the 
moon or the sun? If you make 
a rough calculation to see, would 
you compare the direct gravita- 
tional pulls of the moon and sun 
on a piece of the earth's water? 
If you do, you'll find that the 
sun is the dominant body. 

Why are there spring tides, 
which are the larger than average 
tides near the times of new and 
full moons, and neap tides, which 
are the lower than average tides 
near the first and third quarters 
of the moon? 

399, pp. 15-16; 661, pp. 156- 
159; 662, pp. 32-33; 663, pp. 

23-24, 35 ff; 664, pp. 189- 
192; 668. 

angular momentum 


Tidal friction effects 

As a tidal current flows across 
the ocean bottom, energy is lost 
to frictional heating. One con- 
sequence of this energy loss is 
that the earth's rotation slows, 
and the day gets longer. 

Does the energy loss have any 
further effects? A system cannot 
have a change in its total angular 
momentum unless there's an out- 
side torque. There is no such out- 
side torque on the earth-moon 

90 The flying circus of physics 

system, but we've got an earth with 
a decreasing spin. How then is the 
total angular momentum to be con- 

Will this go on forever? Will 
the earth's day continue to get 
longer? Will there be any change 
in the apparent motion of the 
moon? One prediction is that 
some day the moon may travel 
backwards across the sky. 

111; 661 .Chapters 16, 17; 
663, Chapter 1 1; 672; 673. 




Water in a lake often sloshes back 
and forth just as it does in a small 
rectangular trough. The residents 
around Lake Geneva long ago 
noticed this sloshing (called a 
seiche), which can reach three 
feet in amplitude, but they didn't 
understand what determined its 
periodicity or even what caused 
it. What does determine the 
sloshing frequency in a rectangular 
basin? What periodicity do you 
predict for Lake Geneva (average 
depth about 150 meters and 
length about 60 kilometers)? 
Finally, what makes the lake slosh? 

170, pp. 45-46; 580, pp. 138- 
140; 635, pp. 423-426; 661, 
Chapter 2; 662, pp. 62-65; 663, 
pp. 7-8; 664, pp. 272-273. 

shock fronts 

water waves 

wave speed 


Tidal bores 

In most rivers emptying into 
the sea, the tidal rise is calm, 
perhaps even imperceptible. 
But in others the rise becomes so 
rapid that an almost vertical wall 
of water, a bore, races up the 
river with great force (Figure 
4.56). The English rivers Severn 
and Trent and the Canadian river 
Petitcodiac experience these water 
walls. The bore of the Amazon 
is an awesome sight, being a mile 
wide at places and up to 16 feet 
high, sweeping upstream at 12 
knots. The most striking of them 
all, however, is the bore of the 
Chinese Tsien-Tang-Kiang , 

which has risen as high as 25 
feet. The Chinese skillfully use 
the bore to float their junks 
upstream, ignoring the danger 
and the helter-skelter ride. Why 
do these bores form, and why 
don't all sea coast rivers have 
them ? Does their speed depend 
on their height or the depth of 
the river? 

399, pp. 33-66; 635 pp. 320, 
326-333, 351 ff; 661, 
Chapter 3; 662, pp. 97-98; 663, 
pp. 8, 120-125; 664, pp. 320- 
321; 674 through 676. 

Figure 4.56 

Tidal bore racing up river. 

The madness of stirring tea 9 1 


wave flow 

water waves 


New A 


46 ft 


U.S.\ Canada 


Maine \ 



Bay 1 

St. John * 

A ^ 1 

125 ft Minas [ 
o\ 1 Basin 

51 ft 


Nova Scotia 

f 10 ft 


{■\' ;: ^yl- ■"-'■■■:'■ • ••:• : -••.:- v-V : : ■;■■•'•=' 

Miles ' 

Figure 4.57 


Tidal range in the Bay of Fundy. 

Bay of Fundy tide 

Why does the Bay of Fundy in 

range is not too large, about 10 

tidal range? What would such a 

Nova Scotia (Figure 4.57) have the 

feet during spring tides. Further 

length be for a bay whose depth 

world's largest tidal range (the 

up the Bay at St. John the range 

is like that of Fundy (75 meters)? 

change in water height due to the 

increases to 25 feet, and at the 

How does that compare with 

tides)? In some places the range 

end of Chignecto Bay it is 46 feet. 

Fundy 7 s actual length? 

is so large that men fish by erecting 
large nets during low tide and 
then during the next low tide, 
simply collecting the fish caught 

The largest range, 51 feet, is found 
at the end of the Minas Basin. 
(Winds can add as much as another 
6 feet to these figures.) 

399, pp. 27-29; 663, pp. 1 13- 
1 15; 664, pp. 235-236; 670; 

in the net during the high tide. 

Can a bay have an especially 

At the mouth of the Bay, the 

favorable length to enhance the 

92 The flying circus of physics 

shock front 

water waves 

wave speed 


Sink hydraulic jump 

When a stream of water falls into 
my sink, the water spreads out in 
a relatively thin layer until it 
reaches a particular distance from 
the stream where the water sud- 
denly increases in depth. Hence, 
a circular wall of water surrounds 
the stream (Figure 4.58). The 
same type of wall is made if the 
stream falls onto a flat plate, 
though the depth change is not as 
pronounced. What causes these 
jumps in water depth? What 
determines the radius at which a 
jump occurs? How high is the 

635, pp. 324 ff; 677 through 

Figure 4. 58 

Hydraulic jump in the sink. 

Figure 4.59 

Standing waves in falling water 



Standing waves in falling stream 

If you hold your finger or the flat 
of a knife in a thin water stream, 
a standing wave appears in the 
stream* (Figure 4.59). Why? 
What determines the spatial peri- 
odicity of this wave? Why does 
that periodicity depend on the 
distance between the flat sur- 
face and the faucet? 

^Elizabeth Wood, personal communica- 


Beach cusps 

Why are cusplike formations, 
sometimes outlined on a side with 
small pebbles, very often found on 
sandy beaches (Figure 4.60)? 
Shouldn't the ocean waves striking 
smooth beaches be plane waves? 
Although some cusps are isolated 
and can be dismissed as flukes, 
there are many long beaches 

whose entire length is embroidered 
with periodically spaced cusps. 
What causes them? 

629, pp. 386-389; 648, p. 5490; 
650; 682 through 691. 

Ocean waves 


W$&$M : -'r ^■'■^ Beach £::^$ 

Figure 4.60 
Beach cusps. 

forces in rotating frame 



Ekman spiral 

Suppose there is a steady wind 
blowing over the water somewhere 
in the middle of the ocean. In 
what direction is the net total mass 
transport of water by the resultant 
current? In the direction of the 
wind? Slightly to the left? Well, I 
understand that it is 90° to the right 
in the northern hemisphere and 90° 
to the left in the southern. Why 
90°? The current off the California 
coast provides an example of 
this in shallower water. The winds 
there usually blow southward and 
parallel to the coast, but the top 
layer of the ocean moves toward 
the west. 

580, pp. 76-79; 692. 

The madness of stirring tea 93 


noninertial forces 



Stronger ocean currents in the west 

Doesn't it strike you as odd that in 
both northern and southern 
hemispheres there are stronger 
ocean currents along the western 
sides of the oceans? 
North Atlantic: Gulf Stream 
South Atlantic: Brazil Current 
North Pacific: Kuroshio 
Indian Ocean: Agulhas Current 
(The one exception is in the South 
Pacific, for there is no such large 
current off Australia.) Why is the 
west favored for strong currents? 

666, p. 1025; 692 through 696. 

secondary flow 

centrifugal force 



Tea leaves 

Why do leaves in a cup of tea col- 
lect in the center of the cup when 
you stir it? Since the tea is rotating, 
you may want to class this as just 
another centrifuge example, but 
wait— in a centrifuge don't the 
denser objects move outward? 
Hence, the centrifuge argument 
will only make the behavior of the 
tea leaves even more mysterious. 

44, p. 189; 73; 700, pp. 84-85; 

secondary flow 

centrifugal force 



River meander 

Natural streams and rivers, especial 
ly the older ones, are rarely straight 
for any great length; they almost 
always meander back and forth 
(Figure 4.64). In some cases the 
weaving is so extreme as to cut 
off and abandon a loop, forming 
what is called an oxbow lake. Of 
course, the local terrain may force 
some sinuosity, but even still, 
shouldn't there be many more 
straight sections? What causes the 

44, pp. 189- 190; 73; 360, pp. 
43-48; 364, pp. 78-79; 453, p. 
146; 697, pp. 82-85, Chapter 
9; 698, pp. 56-58; 699, pp. 
144- 145; 700, pp. 84-87; 701 
through 715. 

fluid flow around obstacle 

pressure gradient 

forces in rotating frame 

Figure 4. 64 

Figure 4.65 

If the ball is released in the center 
of the rotating water, it takes 
longer to rise. 


Rising ball in rotating water 

Adjust a small ball's density (by 
partially filling it with water) so 
that it takes about 2 seconds to 
ascend through four inches of water. 
If the water is on a rotating turn- 
table and the ball is on the center 
axis (Figure 4.65), the ascent time 
should be the same, shouldn't it? 
But as a matter of fact, if the 
rotational speed is 33 1/3 rpm, 
a four-inch ascent will now take 
about 30 seconds. Why is there 
such a big difference in rise time? 
Indeed, why is there any difference 
at all? 

717 through 719; 1482. 

94 The flying circus of physics 

pressure gradients 

centrifugal force 


Taylor's ink walls 

If a drop of dyed water is placed in 
a glass of clear water, the dyed area 
will be about half a centimeter 
large. But if the drop is placed off 
center in a glass of water that is 
sitting on the center of a rotating 
turntable, the dyed area will be 
compressed into a thin vertical 
sheet that spirals around the center 
of the glass (Figure 4.66). What 
keeps the dye in such a sheet and 
prevents it from mixing with the 
clear water? 

717; 720. 

Figure 4.66 

Taylor's ink wall in a rotating 

glass of water. 


coriolis force 

angular momentum 


Bathtub vortex 

Do northern hemisphere bathtubs 
really drain in a counterclockwise 
sense, as is commonly believed? 
If bathtubs do drain in opposite 
senses in the two hemispheres, 
does that mean the water doesn't 
rotate at all on the equator? 

72/721 through 736. 



Tornadoes and waterspouts 

Do tornadoes and waterspouts 
turn in any particular direction, 
as do hurricanes? What makes 
them visible? Does water go up 
or down in waterspouts? Why 
do some tornado funnels hop 
along? Do adjacent funnels attract 
or repel each other? Finally, why 
do some funnels appear to be 
double layered, as if they con- 
sisted of two concentric funnels?* 

226; 737 through 746; 1538. 

*For more information on tornadoes, 
their cause and behavior, see Refs. 224, 
225, and 747 through 750. 


Soda water tornado 

Place a recently opened bottle of 

soda water on a turntable's center 
and spin it at 78 rpm. Bubbles 
emerge from the soda water as you 
would expect, but when you add 
a small amount of sugar or some 
other granular substance, a tornado- 
like structure develops. What 
causes this vortex, and what pro- 
vides its energy? 

751 through 754. 



Coffee cup vortex 

Carefully stir a cup of hot coffee 
until you have a uniform swirl 
and then carefully pour a stream 
of cold milk into the center. A 
vortex will form in the center and 
a dimple may be noticeable. But 
if hot milk is used, the vortex will 
not develop. Why is there a vortex 
in the first case and not in the 





Dust devils 

What drives dust devils, those 
whirlwind vortices that are often 
seen in deserts or other places 
with loose sand debris? Does their 
internal air move up or down, and 
is there a preferred sense of rota- 
tion as in hurricanes? How can 

The madness of stirring tea 95 

Figure 4.71 
Dust devil 

seemingly small, local changes in 
the air trigger them? For instance, 
a jackrabbit tearing across the 
desert floor can leave a trail of 
dust devils. Why do nearly all dust 
devils die within only three or 
four minutes? Is it because of tur- 
bulence, or is the energy source 
removed? Finally, why are they 
shaped like an uneven hourglass 
(Figure 4.71) and not like a tornado 

756 through 764; 1539; 1540. 


Fire vortices 

Why do tornadolike vortices fre- 
quently develop near volcanos, 
forest fires, and large bonfires? 

765 through 772. 


Steam devil 

There is yet another natural vortex, 
but it is rarely seen. In the dense 

steam fog over some winter lakes, 
such as Lake Michigan, steam devils 
appear. You can simulate this by 
allowing cold air to blow over a 
bathtub full of warm water in a 
moist bathroom. What drives the 
steam devils? 

773; 774. 


Vortex rings from falling drops 

If a drop of dyed water falls into a 
glass of clear water, you can see the 
vortex ring created by the splash 
and watch the ring as it expands 
and descends (Figure 4.74). Can 
you explain in simple terms why 
the ring is formed and why it 
expands? Which way does the 
fluid rotate in the ring? Finally, 
why are more (but less pro- 
nounced) rings also created by 
the same splash? 

155 f p. 103; 775; 776 ', pp. 
522-526; 777. 



Figure 4. 74 

Falling and expanding vortex 

ring of dyed water. 


Ghost wakes 

If you quickly move a vertical 
piece of cardboard horizontally 
across a pool of water as shown 
in Figure 4.75a, two wakes will 
appear on the pool's surface. 
Why? If the cardboard is moved 
to the side as shown in Figure 
4. 75b, only one wake appears. 
Again, why? 


Figure 4. 75a 

Top view of moving cardboard 

and vortices. 

Figure 4.75 b 

Top view of moving cardboard 
and vortex. [Both figures after 
C. W. McCutchen, Weather, 27, 
33 (1972).] 

96 The flying circus of physics 

adiabatic process 




Hot and cold air vortex tube 

The Ranque-Hilsch vortex can 
mysteriously separate hot from 
cold air without any moving parts. 
If compressed air (at room tem- 
perature, say) is forced into the 
vortex tube through the side 
nozzle (see Figure 4.76), air as 
hot as 200°C will emerge from 
one arm of the vortex tube while 
air as cold as — 50° C escapes from 
the opposite arm. There are no 
heating-cooling mechanical de- 
vices inside the tube, just a cir- 

cular cavity with a center escape 
hole on one side and a valve at 
the end of the arm on the other 
side. How is the temperature 
difference created by this simple 
arrangement? Must we have a 
little man stationed in the tube, 
feverishly sorting out cold and 
hot air from the room-temperature 

778 through 787. 

Hot air 



Cold air 


Figure 4. 76 

Compressed air blown into vortex tube separates into hot and 

cold air. 




Birds flying in V formation 

Do you think there is any physical 
reason for the V formation assumed 
by migrating birds? Or do you 
think it is simply an interesting be- 
havioral response and serves no 

real purpose? If, perhaps, there 
is some aerodynamical basis for the 
formation, is it important that the 
formation be symmetric? Is it 
necessary that the birds synchron- 
ize the flapping of their wings? 
What advantage would the V for- 
mation have over any other forma- 
tion (line abreast or zigzag, for 
example)? Why don't birds fly 
in schools like those of fish? 



Sinking coin 

If a coin is dropped into a large 
container of water, will it sink with 
its edge or flat side downward? 
Will the same thing happen in a 
viscous fluid such as oil or a sugar 
solution? How will a cylinder 

Common sense probably tells you 
a sinking object will always assume 
the most streamlined orientation. 
However, for some parameters a 
coin and cylinder will sink in 
water with whatever orientation 
you initially give them. Making the 
disc larger or the fluid more 
viscous causes the disc to fall broad- 
face. What forces the disc to pre- 
sent its broadest side? Why aren't 
smaller coins and cylinders also 
forced into the broadside orienta- 

788 through 790. 



Tailgating race cars 

In stock car races what advantage 
is there for one car to tailgate 
another car (called drafting)? Is 
the lead car affected at all? When 
the trailing car suddenly pulls out 
to pass, why does it receive a 
whiplash acceleration around the 
lead car? 


The madness of stirring tea 97 







Several sinking objects interacting 

Figure 4.80a 

Two views of two cylinders falling 

in a viscous fluid. 

Several objects may interact in 
strange ways while sinking in vis- 
cous fluids such as oil or a sugary 
solution. Here are three examples. 

Into a viscous fluid, drop two 
cylinders, one closely following 
the other. For certain ranges of 
viscosity and cylinder size and 
speed, the trailing cylinder may 
catch the leader and rotate about 
it until they are horizontally paral- 
lel, and then they will both rotate 
together and separate horizontally 
as they sink (Figure 4.80a). 

In a simpler interaction, two 
discs dropped after a leader disc 
may catch the leader, and then 
the three will take on a stable 
butterfly configuration (Figure 

Also, a compact cluster of three 
to six spheres will separate them- 
selves into a horizontal, regular 
polygon, and this polygon will 
slowly expand as it falls. 

Without getting into too much 
detail, can you roughly explain 
why each of these interactions 
take place? 

789 through 793. 

Figure 4.80b 

Butterfly configuration of three 

discs falling in a fluid. [After 

K. O. L. F. Jayaweera and B. J. 

Mason, J. Fluid Mech., 22, 709 



Strange air bubbles in water 

Closely examine bubbles rising 
through a glass of water. The very 
tiny ones (with radii less than about 
0.7 millimeter) are spherical and 
rise to the surface in a straight line 
just as you would guess. Slightly 
larger bubbles (up to 3 millimeters 
in radius) are spherical but either 
zigzag or spiral upward. If the 
radius is even larger (more than 
3 millimeters), the path is again 
straight, but for radii greater than 
1 centimeter, the bubbles look like 
spherical caps and resemble umbrel 
las (Figure 4.81). 

Why does a rising bubble's shape 
depend on its size? What forces 
the intermediate size bubble to 
zigzag and spiral, and what param- 
eters fix the frequency of that 

776, pp. 367-370, 474-477; 
796 through 801. 

Figure 4.81 

A large bubble rising in water 

resembles a spherical cap. 

98 The flying circus of physics 




Fish schooling 

The schooling of fish certainly 
must have roots in social factors, 
but it must also offer a practical 
advantage to the fish, for when 
swimming in such a school, a 
fish's endurance is considerably in- 
creased, perhaps as much as six- 
fold. Why would there be an ad- 
vantage for fish of similar size 
and shape to swim in regular 
arrays and in synchronous motion? 
In particular, what determines the 
distance between fish? Should 
one fish swim directly behind 
another? Why don't fish swim 
in the V formation that birds use? 




Wind gusts on building 

Why is the windward side of a 
building calmer than the rear in a 
strong and gusty wind? Shouldn't 
just the opposite be true? 

453, pp. 138-139. 

driven resonance 

harmonic oscillations 


Tacoma Narrows Bridge collapse 

You may have heard of the failure 
of the Tacoma Narrows suspension 
bridge, because physics depart- 
ments often have the spectacular 
film (1562) showing the bridge 
oscillating and eventually col- 
The bridge began its oscillations 

Figure 4.82 

"It all started with an innocent 

game of follow -the-leaderl" 

even when it was being built; in 
fact, the structure's rippling motion 
made the bridge workmen seasick. 
After it was opened to traffic, the 
motion was so pronounced that 
motorists came from miles away 
just for the thrill of being on the 
bridge. On days when the bridge 
oscillated as much as five feet, 
motorists on the bridge actually 
disappeared from each other's 

Still, the bridge's collapse came 
as a complete surprise. Suddenly, 
on the morning of the collapse, 
the ripple ceased, and after a brief 
pause, the bridge went into a 
furious torsional oscillation. Two 
people on the bridge at the time 
crawled on all fours to escape. 
After trying to rescue a dog 
abandoned on the bridge, a pro- 
fessor could retreat only along the 
nodal line of the torsional oscil- 
lation. (His retreat is seen in the 

After 30 minutes of torsional 
motion a floor panel fell from the 
main deck. Another 30 minutes 
brought another 600 feet of deck 
down. Though the twisting then 
ceased briefly, it began again, and 
it took only several additional 
minutes to bring the remaining 
deck down. 

The bridge designer (who died 
shortly after this tragic end to his 
career) could hardly be faulted, for 
at the time there was scant under- 
standing of the aerodynamic be- 
havior of suspension bridges. The 
repercussions in bridge building 
were enormous and long lasting. 

The bridge failure is introduced 
in the physics classroom as an 

The madness of stirring tea 99 

example of driven resonance. Al- 
though the wind was not blowing 
unusually hard that day, the 
bridge's oscillations grew in 
strength to catastrophic pro- 
portions. But why and how ex- 
actly did the wind do this? How 
would a fairly steady wind cause 
the rippling, which soon led to the 
torsional oscillations? Why would 
longitudinal oscillations be created? 
Since driven resonance implies a 
certain frequency match between 
the driving force and driven object, 
you must explain how the wind 
produced that frequency match. 

How can a bridge's aerodynamic 
instability be minimized? One 
new feature resulting from the 
collapse was the placement of 
longitudinal gaps in the bridge's 
roadway, say, between the op- 
posing lanes of traffic. Why would 
this help stabilize the structure? 

802 through 812; 1556. 

Kelvin-Helmholtz instability 



Air turbulence 

What causes the bumps so fre- 
quently encountered by jet air- 
craft? Some disturbances are 
single jolts. Some force the air- 
plane up and down as if it were 
a ship at sea. Others quickly 
heave the airplane to a different 
altitude, perhaps making the 

pilot lose control as a result. 
Often there are warning signs for 
these various types of disturbances, 
but some turbulence can occur in 
clear weather, with no clouds, and 
at altitudes of several kilometers. 
This turbulence was unknown 
until jet airplanes of World War II 
were first able to reach the relative- 
ly high altitudes at which it takes 
place. What is responsible for 
the clear air turbulence and the 
other types of disturbances? Why 
is it experienced primarily at 
higher altitudes? 

819 through 822. 


Watch speed on a mountain top 

Why will a spring-driven watch run 
at a different speed on a mountain 
top than at a sea shore? 

9, pp. 80-82. 



Wire mesh on faucet 

Why is a wire mesh often placed 
over a faucet's outlet? It will, 
of course, catch small stones in the 
water supply, but people claim the 
water is also "smoother" or 
"softer" with the mesh in place. 
Why would that be? 


wave interference 


Fast swimming pools 

Why are some swimming pools said 
to be fast? Could different depths, 
different splash gutters, chemical 
additives, etc. noticeably influence 
a swimmer's speed? 

edge oscillations 


Nappe oscillations 

When water is discharged over the 
spillway weirs of some dams, the 
falling water curtain may go into 
severe oscillations (Figure 4.89). 
The noise from the oscillations, in 
addition to the normal noise from 
water impact at the dam's foot, 
may even make the vicinity un- 
bearable. What causes these oscilla- 
tions, and why is there so much 
extra noise? 

813 through 816. 

Figure 4.89 

100 The flying circus of physics 


flow around obstacle 

driven pendulun 

particle transport 


Parachute holes 

Why do parachutes often have 
central holes (Figure 4.90a), 
especially the conventional para- 
trooper parachutes? Isn't a hole a 
rather strange thing to have, for 
wouldn't you think it would be 
counter to the whole point of a 
parachute? If the hole is to reduce 
drag, why not just make the para- 
chute smaller? 

Some of the unconventional 
parachutes need even more ex- 
plaining. For instance, some on 
stock car racers resemble two 
crossed-bandage strips (Figure 

4.906). Why would someone use 
such a drag chute? Wouldn't the 
drag be quite low? 

Even in the absence of gusty 
winds, men using conventional 
parachutes swing to and fro 
during their descent. Since such 
swinging can be very dangerous 
during the landing, the men ob- 
viously are not doing it on purpose. 
What causes the swinging, and what 
determines its period? 

817; 818. 

Figure 4. 90a 
Conventional parachute. 

Figure 4.90b 
Stock-car parachute. 


momentum transfer 

hydrostatic forces 


Speed of a drifting boat 

A drifting boat is commonly 
thought to travel faster than 

the stream. Indeed, since a 
drifting boat can be steered, 
doesn't it have to? But how 
can the boat, which supposedly 
is just being pushed along by the 
stream, be moving faster? 

453, p. 179; 824; 825. 



The gaps in snow fences 

If you want to stop snow drifts 
near a roadway, railroad track, 
or walkway, why do you put up 
a snow fence. . .why not a snow 
walR Granted a fence may be 
less expensive, but wouldn't a 
wall do a better job than a fence 
with all its gaps? 

453 ', p. 334; 600; 826. 

flow around obstacle 

particle transport 


Snow drifts 

Snow drifts are much more pro- 
nounced around posts and trees 
than on the wind-facing sides of 
houses. Why is there such prefer- 
ential unloading of drifting snow 
around the narrower obstacles? 

364 , pp. 12- 13; 453, p. 333; 


eddy formation 


Streamlined airplane wings 

Why are the trailing edges of air- 
plane wings sharp? (To say that 
it's just for streamlining is not 
enough.) Why do some planes have 
swept-back wings and others not? 

603; 605. 

The madness of stirring tea 101 

air drag 


Skiing aerodynamics 

Aerodynamically, what is the best 
position a skier can assume in a 
downhill race? Winners in the 
Olympics and other world meets 
are often determined by time dif- 
ferences between skiers of as little 
as 0.01 second. Because of the 
crucial need for sound knowledge 
about the stance as well as the 
equipment of a skier, the French 
conducted wind tunnel experi- 

ments and developed the "egg 
position" (Figure 4.95a). Al- 
though this in not the best posi- 
tion for drag reduction, it is a 
practical one to assume in a 
strenuous race. 

How about the other two posi- 
tions shown ? Before the testing 
a good many of the skiers had in- 
stinctively adopted the lowest pos- 
sible position, dropping the arms 

alongside the legs (Figure 4.95b). 
As it turned out, the high crouch 
(Figure 4.95c) gives remarkably 
less drag than the lower crouch 
with lowered arms-but still not 
as little as the French egg position. 


Figure 4.95 

Three skiing positions. 

air drag 


Dimpled golf balls 

Why are golf balls dimpled? In the 
very early days of golf, the balls 
were smooth, and it was only ac- 
cidentally discovered that scarred 
balls traveled further than the 
smooth, unscarred ones. If today's 
dimpled ball is driven, say, 230 
yards, a smooth ball similarly struck 

would travel only 50 yards. Does 
this make sense? Shouldn't the 
smoother ball go further because 
it will have less air drag?* 

593; 827; 828. 

*ln the last few years a newer golf ball 
design— one with randomly spaced, 
hexagonal dimples rather than the old, 
regularly spaced, circular dimples— has 
been sold with the claim of an addi- 
tional six yards in average flight distance. 

air pressure 

momentum transfer 


Flight of the plucked bird 

How do birds fly? Yes, I know 
they flap their wings up and down, 
but how does that keep them 
aloft and moving forward? Well, 
maybe the bird flaps backwards 
on the downstroke, thereby pro- 
pelling itself forward. No, slow 
motion movies show the wing 

1 02 The flying circus of physics 

moving forward not backward, on 
the downstroke. Perhaps the best 
clue to the bird's flight lies in the 
ancient Greek myth of Icarus who 
flew too close to the sun, lost the 
feathers glued to his arms, and 
then plunged to his death. Must 
a bird have feathers to gain lift 
and forward drive? Can a plucked 
bird fly? 




lift and drag 


Bird soaring 

What allows birds to soar so 
effortlessly and so continuously? 
If they are riding on winds de- 
flected upward by trees and hills, 
for instance, then why can they 
soar just as well over flat land and 
water? If they gain lift by gliding 
into a wind whose strength in- 



Figure 4.99 

Several bridling techniques for kites. 



What keeps triangular and box 
kites aloft, and which type is 
more stable? Why do some kites 
have tails? Finally, what advan- 

tages do the various bridling tech- 
niques shown in Figure 4.99 give? 


creases with height, then why do 
they seem to soar so much better 
on wind-free days? Finally, if they 
ride thermal currents upward, then 
why can you sometimes see one 
group of birds soaring while 
another group, either below or 
above the first group, must flap 
their wings to remain aloft? Be- 
sides, if the lift is produced by 
thermals originating on the 
ground, shouldn't larger birds have 
an easier time soaring near the 
ground? Actually, they can rarely 
soar there. 

Some birds stalk ocean liners 
across long stretches of open water, 
somehow gaining their propulsion 
by gliding near the ship waves. 
How do they do this? 

364, pp. 13- 15, 120- 12 1; 604; 
852, pp. 127-131; 853 through 

roll vortices 




Cloud streets 

Sometimes the sky is covered 
with long, straight rows of cumu- 
lus clouds called cloud streets. 
What orders the clouds this way, 
and in particular what determines 
the spacing between rows? Why 
aren't cloud streets made more 

361, pp. 4- 13, 39, 43; 362, 
pp. 28-30; 364, pp. 154- 155, 
175; 1456. 

The madness of stirring tea 1 03 


row vortices 

surface tension 

gravity waves 

nonlinear fluid flow 




Coffee laced with polygons 

If you examine a hot cup of coffee 
under a strong light that is incident 
nearly parallel to the surface of the 
coffee, you will find the surface 
laced with polygonal cells (Figure 
4.101a). They disappear, however, 

Figure 4.101a 

Polygons on coffee surface. (After 
V. J. Schaefer, American Scientist, 
59 (Sept.-Oct 1971).) 

as the coffee cools. You can also 
destroy the cellular appearance 
by putting a charged rubber comb 
(charge it by running it through 
your hair) near the coffee. 

Other liquids show surface 
designs too. James Thomson, a 
famous Nineteenth— Century phys- 
icist, noticed the rapidly varying 
surface designs in a pail of hot 
soapy water and in strong wines. 
Later, the Frenchman Bernard was 
able to make regular patterns in 
oil surfaces when the oil was heated 
from below. His regular polygons 
would slowly evolve into a beauti- 
ful hexagonal, honeycomb struc- 
ture (Figure 4.1016). Still other 

Figure 4.101b 
Hexagonal Bernard cells. 

fluids gave a roll-like appearance 
(Figure 4.101c). Recently, cellular 
surface designs were attempted on 
board spacecraft while under zero 

Figure 4.101c 

Surface with roll-like structure. 

In these examples, why do rolls 
and polygons (especially honey- 
combs) form on the fluid surfaces? 
Is the same physics actually re- 
sponsible for all of the examples? 
Why do the coffee cells disappear 
when there is a charged body near- 
by? Finally, do these several types 
of surface designs depend on 

360, pp. 93-94; 453, pp. 4 18- 
421; 580, pp. 113-115; 830 
through 849. 


Longitudinal sand dune streets 

Looking down on desert sand dunes 
from a high altitude airplane, one 
sees "curious long, narrow dune 
belts running across the desert, 
roughly from north to south, in 
almost straight lines [Figure 
4.102] ," (863) as if one were 
viewing well-designed parallel 
streets. The dune belts are char- 
acteristic of virtually every major 
desert in the world, and they all 
run roughly north to south and 
have spacing of about 1 to 3 

Leaves scattered over lake sur- 
faces and surface seaweed also col- 
lect into rows, though the scale is 
smaller, with the rows being only 

Figure 4.102 

Sand-dune streets as seen from 

a high altitude. 

1 04 The flying circus of physics 

100-200 meters apart and up to 
500 meters long. 
In these examples what deter- 


ripples or waves. What causes 
those, and again, what determines 
the periodicity of the waves? If 


mines the direction the rows and 


you watch them closely for a long 

belts run? If it is the wind, then 

Sand ripples 

time, you may find them traveling 

do the rows and belts run parallel 

upstream. Why do they do that? 

or perpendicular to it? Moreover, 

Why are the sides of a sand dune 

144; 453, p. 334; 629, pp. 381- 

what determines the spacing be- 
tween them? 

covered with sand ripples? What 

386; 687; 688; 697, pp. 55-59; 

exactly determines the spacing of 

698, pp. 134- 136; 869 through 

580, pp. 18- 19, 1 19- 120; 862 

those ripples? 


through 868. 

The sandy bottoms of streams 
are also often covered with sand 



Smoke ring tricks 

To amuse me during the long 

trailing one expanded and slowed 

pass through the first, and the 

summer days of a small country 

down (see Figure 4.103). Their 

game of chase begins. 

town, my grandfather would blow 

roles were exchanged, and the 

Exactly how are smoke rings 

smoke rings for hours on end. 

new trailing ring then passed 

formed, and how do they retain 

In one of his simpler tricks he 

through the new leading ring. 

their shape for so long? Why 

would send a ring toward a wall, 

This game of leapfrog continued 

does a smoke ring expand as it 

and the ring would expand as it 

until the smoke rings became too 

approaches a wall? Finally, what 

approached the wall. 

dispersed for further play. 

causes the chasing game of two 

His best trick, however, was 

You can see the same thing by 

smoke or water rings? 

blowing one smoke ring through 

dropping a colored drop into a 

another, larger one. After the 

beaker of water. Upon hitting the 

36, p. 1; 51, pp. 161-167; 109, 

speedier trailing ring passed 

surface, the drop forms a ring that 

p. 7; 453, p. 75; 721; 850; 851. 

through the leading one, the 

both expands and descends.* A 

*See Prob. 4.74. 

former leading ring contracted and 

second, closely following drop 

speeded up while the former 

will produce another ring that will 




Figure 4. 1 03 

My grandfather's smoke-ring trick. 

The madness of stirring tea 105 

forces in liquids 


flow around obstacle 

vapor pressure 



How do siphons work? In parti- 
cular, if they depend on atmospher- 
ic pressure, then why can some 
liquids be siphoned in a vacuum? 
Do they depend on gravity? When 
the siphon tube is first lowered into 
the liquid, why doesn't the siphon 
start itself? What force pulls the 
liquid up the first arm (denoted 
A-B in Figure 4.105) against 
gravity? Finally, how is the height 
of a siphon limited, especially when 
the siphon works in a vacuum? 

875; 876. 

Figure 4.105 

*For several curious types of siphons 
devised by Hero of ancient Greece, see 
Ref. 877. 


Dune height = 33 ft 



; 400 ft •: 

; 1958 :■ 

Figure 4.106 

The march of a sand dune over 

26 years. (Adapted from 


Marching sand dunes 

I would have thought winds would 
tend to disperse a sand dune, but 
Figure 4.106 shows a typical case 
in which they marched a dune 
across a desert floor. The dune's 
character and identity remain 

Geology Illustrated by John S. 
Shelton. W. H. Freeman and 
Company. Copyright © 1966.) 

intact even after 26 years of 
travel. How, exactly, are dunes 
moved by the wind? 

144; 453, pp. 333-334; 698, 
pp. 141-142; 699, p. 198. 




The Crapper 

How does a flush toilet work? 
What forces the water, etc. 
(especially the etc.) to enter the 
pipes? When the water from the 
tank comes into the bowl, is it 
merely falling from a water con- 
tainer above? Why do most toilets 
have a second, smaller hole in the 
One of the most interesting books 

I have come across in writing The 
Flying Circus is Flushed with Pride: 
The Story of Thomas Crapper (878), 
It was Crapper who developed the 
flushing toilet. (Obviously he also 
contributed to the American lan- 

Now you may not appreciate 
this, but it was tough work 
developing the flush toilet, and 
serious research was conducted by 
Crapper and others. Of course in 
their experiments these researchers 
had to simulate the actual material 
toilets normally handle. Toilet 
testing must have reached its 
zenith when in 1884 they achieved 

106 The flying circus of physics 

"a super-flush which had 

completely cleared away: 

10 apples averaging 1 3/4 ins. 

in diameter, 

1 flat sponge 4V& ins. in 


3 air vessels, 

Plumber's "Smudge" coated 
over the pan, 

4 pieces of paper adhering 
closely to the soiled surface."* 

A truly remarkable feat of 

253, pp. 334-335; 317, pp. 95- 
97; 3 18, pp. 108- 1 13; 878; 879, 
pp. 260-261. 

*From the book, Flushed with Pride by 

Wallace Reyburn. Copyright © 1969 by 
Wallace Reyburn. Published by Prentice- 
Hall, Inc., Englewood Cliffs, N. J. Per- 
mission also granted by Wallace Reyburn 
and Macdonald & Co. 

drop aerodynamics 


Street oil stains 

On some roads on which the traffic 
speed is sufficiently high, oil stains 
are annular with an unstained sec- 

Figure 4.108 
Street oil stain. 

tion of road in the center of each 
stain (Figure 4.108). With slower 
traffic the stains are just splotches. 
Why do the annular stains appear, 
and how fast must the cars be 
traveling for them to be formed? 

887, p. 187; 888. 

surface films 

boundary layers 


Lake surface lines 

Here and there on the surfaces of 
lakes and streams you can see thin, 
almost invisible lines. They are 
more noticeable if the water is 
flowing because then a small ridge 
of water builds up on one side of 
a line (Figure 4.109). What do 
you think these lines are, and why 
are the ridges formed? 

Powder sprinkled on the ridge 
will reveal a two dimensional flow 
pattern of streetlike channels on 
the opposite side of the line 
(Figure 4.109). What causes such 
a pattern? 


?; 89 A 


ft ill 






i Phi 






Figure 4.109 

The line and ride on a stream 

or lake water (overhead view). 

surface film 


Milk's clear band 

The next time you're mulling 
over a glass of milk, examine the 
milk film at the edge of the milk 
as you tip the glass. Between the 
film left on the bottom of the glass 
and the milk there is a clear area 
a few millimeters wide (Figure 
4.110). Why is the clear band 





Figure 4.110 

The clear band in a tilted glass 

of milk. 

water waves 

surface tension 


Spreading olive oil on water 

In Prosperous Cell (889) Lawrence 
Durrell describes the nighttime 
spear fishing in the lagoons beneath 
the Albanian hills. For spear fishing 
the water must be clear and calm 
because even a slight breeze severely 
distorts the image of the fish and 
ruins the aim. The fisherman can 

The madness of stirring tea 107 

cope with a small breeze, however, 
by sprinkling a few drops of olive 
oil onto the water. Why do these 
few drops calm the water? 

890, pp. 63 1-632; 89 1; 892. 

internal waves 

wave damping 


Marine organic streaks 

Biologically active regions of the 
oceans are often covered with 
long, wide streaks where the 
rippling of the water is suppressed 
by a film of organic material. When 
the illumination is just right, the 
sight can be beautiful. The organic 
streaks apparently do not depend 
on the wind like the seaweed streets 
discussed in Problem 4. 102, for they 
are best seen in a light breeze, not 
a strong one. (The breeze really 
does nothing but heighten the con- 
trast between the size of the ripples 
on the free water and on the streak.) 
What cause the film to form into 
streaks this way? 

895 through 898. 


Splashing milk drops 

When a milk drop splashes on a 
liquid surface, a crater is thrown 
up, eventually breaking into a 
crownlike structure (Figure 4.113). 
As this crown subsides, a liquid 
jet (the "Rayleigh jet") leaps up 




off from 
central jet 

drop is 

Figure 4.113 

After P. V. Hobbs and A. J. 
Kezweeny, Science, 155 (3766), 
1112-1114 (1967). Copyright 
1967 by the American Association 
for the Advancement of Science. 

from the center of the former 
crater, which then pinches off and 
ejects one or more small drops. 
Why does the crater rim break into 
the crownlike formation, and why 

does the central jet form and then 
pinch off drops? The pinching 
itself especially needs explaining. 
Suppose the milk drop experi- 
ment is done in outer space (with 
no gravity). -Will the same type of 
splash occur? In fact, will there 
be any splash at all? 

880 through 886. 

surface tension 


centrifugal force 


Water bells 

If a water stream falls onto the 
center of a disc, the water will 
spread over the disc and form a 
transparent sheet as it flows off. 
The sheet may even close back onto 
the center support of the disc, 
forming a beautiful bell shape 
(Figure 4.1 14). What forces the 
sheet back in like this, and what 
determines the actual shape of 
the bell? 

899 through 904. 

Falling water stream 

Figure 4.114 

108 The flying circus of physics 

surface tension 

momentum conservation 

water waves 


Water sheets 

If two identical water jets are 
directed toward each other, 
beautiful thin sheets of water can 
be produced (Figure 4.115). Why 
do the streams form sheets rather 
than just break up? Why do the 
sheets eventually disintegrate at 
some particular distance from 
the impact point? 

The shape of the edge and the 
stability of the sheet fall into 
three main types which depend on, 
among other things, the rate of 
water flow. For low speeds, the 
sheet is stable with circular edges. 
For the next type, at higher speeds, 
two things can happen: the edge 
may be cusp shaped or waves may 
be set up on the sheet. In the 
third type, for even higher speeds, 
the sheet will flap like a flag in 
the wind. Roughly, what causes 
these differences? 

904 through 910. 

Figure 4.115 

Water sheet formed by collision 
of upward and downward water 
jets. [After G. I. Taylor, Proc. 
Royal Soc, A 209, 1 (I960).] 


Cluing water streams 

Punch several adjacent holes in the 
side of a can, parallel to the bottom. 
Fill the can with water and run your 
finger through the leaking streams. 
For some reason, the streams now 
converge and remain together even 
after you've removed your finger 
(Figure 4.116). What keeps them 

Figure 4.116 

Three water streams seemingly 

glued together. 

surface tension 


Pepper and soap 

If you dip a small piece of soap 
into a bowl of water sprinkled with 
pepper, the pepper will immediately 
race away from the soap. Why? 
How fast do you think the pepper 
grains are moving? 

321; 592, p. 40. 

Bernoulli effect 

boundary layer 

pressure differential 


Pouring from a can 

When I pour my beer, why does 
it insist on running down the side 
of the can instead of falling 
straight down from the lip (Figure 
4.118)? What determines how far 
down it adheres to the can? How 
fast must I pour the beer to 
prevent any such "sticking"? 

Your first impulse will most 
likely be to attribute the pheno- 
menon to surface tension or ad- 
herence of the liquid to the con- 
tainer. However, neither is 
responsible for the spilt beer. 
What is, then? 

911; 912. 

Figure 4.118 

Fluid stream is forced back along 

the c*n. 

The madness of stirring tea 109 

surface tension 

film creep 


Tears of whiskey 

After pouring a shot of whiskey 
into an open glass, you will see a 
fluid sheet that first creeps up the 
side of the glass and then forms 
tear drops around the side. What 
causes that upward creeping to 
such surprising heights? 

832; 848; 849; 1530. 


Aquaplaning cars 

If you lock the brakes on your car 
while moving at high speed on a 
wet road, the car will act like an 
aquaplane. That is, the tires will 
skim along on a thin sheet of water 
and will not actually touch the 
road. Why does this happen, and 
why doesn't it always happen on 
wet roads even when the brakes 
are not applied? Is there any 
tread design that will minimize 
this effect? 


surface tension 


Floating water drops 

Water drops can often be seen 
skimming across a water surface, 

almost miraculously escaping 
consumption by the surface. What 
delays the death of these drops? 

534; 914 through 916; 1608; 


(4.122 through 4.131) 


Soup swirl reversal 

The next time you fix tomato soup, 
give the soup a good swirl in the 
pan and then lift your spoon out. 
The swirl in the soup dies out, as 
you would expect, but during the 
last few seconds the soup turns in 
the opposite direction. What makes 
it do that? 


elastic fluids 


A leaping liquid 

Some hair shampoos * (and 
several other liquids) display a 
curious leaping tendency when 
being poured into a partially filled 
dish. If the falling stream is thin 
enough, the liquid will form a 
small hump near the stream's 
entrance point. Then the stream 
will seemingly leap back up 
from the surface as shown in 
Figure 4.123). Each time this 




Figure 4.123 

[After A. Kaye, Nature, 19 7, 

1001 (March 9, (1963).] 

happens the hump disappears and 
must be rebuilt before another 
leap occurs. What causes the hump 
and the leaping stream, and what 
is so unique about the liquids 
displaying this property? 

917; 921; 922; 923, pp. 249- 

*A. A Collyer, personal communication. 

Weissenberg effect 



Rod-climbing egg whites 

When a glass of water is placed on 
the center of a rotating turntable, 
the surface of the water curves up 
towards the outside of the glass 
because of centrifugal force. The 
same shape is also obtained if the 
glass is held fixed and a rotating 
rod is inserted along the central 
axis of the glass. 
Not all fluids, however, behave 

110 The flying circus of physics 

in this common-sense way. Egg 
whites, for instance, will have the 
proper curved surface on a rotating 
turntable but will behave strangely 
with the rotating rod. Rather than 
curve up toward the outside, the 
egg white will climb the rod 
(Figure 4.124). Gelatin dissolved 
in hot water will show normal be- 
havior at first, but as the mixture 
cools, it will begin to display this 
strange urge to climb the rod. 
Since the centrifugal force is 
certainly still present because 
of the rotation there must be an 
even stronger force pulling the 
fluid inward and up the rod. What 
is this force? 

917; 92 1; 923, pp. 23 1-236; 
924, p. 375; 925, p. 121 ff; 
926, pp. 52-53; 927, p. 671; 
928, pp. 522-524; 929 
through 934; 1620. 

Figure 4.124 

Egg white climbing the stirring rod. 

viscous fluid flow 


Liquid rope coils 

If you pour thick oil, honey, or 
chocolate syrup onto a plate from 

a reasonable height, the stream will 
begin to wind itself up a short dis- 
tance above the plate (Figure 
4.125). Why does this coiling 
occur, and what affects the dia- 
meter and height of the coil and 
the rate at which if forms? 

918 through 920. 


Stream forcing 

itself into 

a coil 

Liquid level 



Figure 4.125 

Liquid rope coil. [After G. 
Barnes and R. Woodcock, Amer. 
J. Phys., 26 (4), 205 (1958).] 



sol-gel change 


Thixotropic margarine 

Many common, household fluids 
would be useless if they were not 
thixotropic, that is, if their vis- 
cosity did not decrease when the 
fluids were subjected to shearing 
forces. For example, margarine 
would not spread very well at 
room temperature were it not 
for its decrease in viscosity when 

being sheared by the knife. Thixo- 
tropy is just as important in 
painting with one-coat paints. 
The paint must be viscous enough 
to give a smooth coat without 
running, so the viscosity must 
be low when the paint is 
sheared by the brush. But it 
must increase quickly enough 
after brushing to prevent running. 
There are many other thixotropic 
fluids: ketchup, gelatin solutions, 
mayonnaise, mustard, honey, and 
shaving cream. What effect must 
shearing forces have on the struc- 
ture of these liquids to cause the 
decrease in viscosity? 

/ 10, pp. 185- 186; 92 1; 923, pp. 
246-248; 924, p. 374; 925, pp. 
144- 149; 930; 934; 935, pp. 
405-407; 936 through 938; 1547. 



Die-swelling Silly Putty* 

Do you expect a fluid to change 
its volume as it emerges from a 
pipe through which it is being 
pushed? Most fluids don't, their 
diameters upon emerging being 
the same as the pipe's inside 
diameter. An exception, however, 
is Silly Putty, a silicone putty 
sold in toy stores. Pack a small 
tube full of Silly Putty, let it 
stand for a while to settle, and 
then push it through the tube. 
As soon as it emerges, it expands 
noticeably (Figure 4.127). Such 
an effect, called die swell, ob- 

The madness of stirring tea 111 

Figure 4.127 

The Silly Putty expands when 

pushed from the tube (die swell). 

viously stems from a peculiar 
property of this fluid, the Silly 
Putty, but what exactly 
causes it to swell, what other 
fluids respond similarly, and why 
don't all fluids behave this way? 

917; 921; 923, pp. 242-244; 
935, pp. 405-407; 1620. 

*® Silly Putty Marketing, Box 741 , New 
Haven, Conn., U.S.A. 


Bouncing putty 

Silicone putty also displays several 
seemingly incompatible properties. 
Hit it with a hammer, and it shat- 
ters. Bounce a ball of it, and it 
bounces better than a rubber ball. 
Leave a ball of it undisturbed, and 
it will gradually flatten. Ap- 
parently it behaves like a liquid 
but demands certain response 
times to external forces. Accord- 
ingly it will shatter if struck 
quickly or will bounce elastically 
if hit a bit slower. Gravity acting 
for a long time will cause it to 

flow. What is it in the putty's 
structure that determines such 
response times? 

917; 923, pp. 236 ff; 939. 




Self-siphoning fluids 

Some fluids, such as polyethylene 
in water,* can siphon themselves 
out of containers (Figure 4.129) 
if you will only initiate the siphon 
ing by pouring out some of the 
fluid. What pulls such a liquid 
over the wall of the container, 
and what holds the stream together? 

9 17; 940. 

Figure 4.129 

A fluid that can siphon itself 

out of the glass. 

*Collyer (917) gives directions for 
making such a fluid. Also see Edmund 
Scientific Company, 430 Edscorp Bldg. 
Barrington, New Jersey 08007, U.S.A. 

hydrostatic pressure 




If you discover yourself stuck in 
quicksand, why is lying down on 
your back the best thing to do? 
(Once you lie down and free your 
legs, you can then roll toward 
shore.) If you should have to pull 
yourself, someone else, or an 
animal out of quicksand, why is 
it best to pull slowly? Does the 
viscosity of the sand change when 
you pull more quickly? If so, 
why? Why do deeply entrenched 
people and animals have bulging 


fluid flow 



Unmixing a dye solution 

If a drop of dye is mixed into a 
solution by rotation, is there 
any way to unmix it? 

Between two coaxial glass cyl- 
inders of nearly the same diameter, 
pour some glycerol and then care- 
fully add several drops of dye 
(Figure 4.131). Rotating the inner 
cylinder 10 times or so apparently 
mixes the dye pretty well. How- 
ever, if you turn the cylinder back 
the same number of turns, the 

112 The flying circus of physics 

After putting drop of dye into the 
glycerol between the cylinders, 
carefully rotate the inner cylinder 
10 times one way and then 10 
times back 

Figure 4.131 

The two cylinders for unmixing 
a dye solution. (The space 
between the cylinders has been 
drawn large for clarity.) 

dye unmixes itself back to ap- 
proximately its initial distribution. 
Why? If you wait too long to make 
the reverse turns, this won't happen. 
Again, why? 

942; 943. 

The madness of stirring tea 113 

She comes 
in colors 


i A ■ ■ 


Ray Optics 

shown in Figure 5.3. Why is there 
a gap, and what determines its 

(5.1 through 5.47) 

951; 952. 


Coin's image in water 





Swimming goggles 

If you place a coin in a trans- 
parent, open jar filled with water 

Why is it that when you are 

and look down through the water 

swimming underwater you can see 

surface from the appropriate angle, 

much better if you wear goggles? 

Figure 5.2 

you can see the coin's image on the 

A particular Central American 

The invisible man. 

surface of the water (Figure 5.4). 

fish, the Anableps, seems to have 

chosen value (Figure 5.2). What 

Putting your hand on the far side 

the best, or the worst, of both 

do you think the value was? No 

of the jar usually has no effect on 

media, for it swims just beneath 

one was able to see the invisible 

the image, but if your hand is 

the water surface with its large 

man. Could such an invisible 

wet, the image will disappear. 

eyeballs protruding above the 

man, with that value of the 


surface. Each eyeball is thus half 

index of refraction, see any- 


in and half out of the water. 

thing at all himself? 

Considering your need of goggles 

to see underwater, how can the 


fish see in both air and water this 


Playing with a pencil in the tub 

170, p. 534; 332, Vol. 1 , p. 36- 

If your bathtimes have become 

3; 462, p. 1 16; 944; 945; 1570. 

dull and uneventful and you need 
something to spice them up, 
bring a pencil along and examine 


its shadow on the bottom of the 

The invisible man 

tub. If you dangle the pencil 

half -submerged, you will find 


The invisible man in H. G. Wells' 

that the shadow does not entirely 

famous novel was invisible because 

resemble a pencil. Rather, it 

he changed his body's index of 

looks like two rounded rods 

refraction to an appropriately 

separated by a white gap as 

Exceptionally good references: Min- 


naert's book (954) is absolutely first 

class; his paper (991 ) updates the book. 

O'Connell's book (966) on the green 

Figure 5. 3 

Shadow of a partially submerged 

pencil [After C. Adler, Am. J. 

flash is fascinating. Also, Wood (360), 
Larmore and Hall (983), and Weather 
(a journal). 

Figure 5.4 

Reflection of coin in side of 

Phys., 35, 774 (1967)]. 

glass of water. 

She comes in colors everywhere 115 


I >H 

Figure 5.5 


Distance of a fish 

If you look down at a fish in a 
tank of water, you will see it at an 
apparent depth which is not as 
great as its actual depth. Is the 
apparent horizontal distance to the 
fish also distorted? The horizontal 
distortion may depend on whether 
you use one eye or two. Try it 
out by placing some object in a 
shallow dish of water and looking 
at it from a distance with your eyes 

nearly level with the surface of the 
water (Figure 5.5). First judge the 
object's distance with your head 
upright and then with your head 
tilted 90°. If the distance seems 
different depending on the posi- 
tion of your head, can you ex- 
plain why? 

946 through 949. 


Ghosting in double-walled windows but also dan gerous. Assuming 

some realistic situation, can 

What causes the double image, 
ghosting, of distant objects in 
double-walled windows? Under 
critical conditions, such as in air 
traffic control at airports, the 
ghosting can be not only annoying 

you calculate the angular separa- 
tion of a true image and its ghost? 
How will the separation vary with 
time of day and weather conditions? 



Mountain looming 

There are places in the world 
where, in late afternoon and early 
evening, mountains can be seen 
rising out of the horizon on the 
ocean. The mountains are real, 
but they are too distant to be seen 
normally. First, in the early 
afternoon, a hazy patch peaks 
above the horizon. Then, as 
the afternoon wears on, the patch 
grows, quickly sharpening into 
obvious mountains near sunset. 
The individual peaks can even be 
recognized. How is this type of 
mirage created? 

164, p. 469; 165, p. 164; 954, p. 
41; 957 through 960. 


Fata Morgana 

Fata Morgana is the most beautiful 
of all mirages, and though it is very 
rare in some areas, it is common in 
the Straits of Messina between Italy 
and Sicily. When there is a layer 
of cold air over warmer water, one 
may see fairy castles rising out of 
the sea, constantly changing, 
growing, collapsing. According to 
legend, the castles were the crystal 
home of Morgana the fairy. This 
mirage is the most difficult of the 
mirages to explain because there 
are several competing effects in- 
volved, but can you unravel the 

164, pp. 474-475; 954, pp. 
52-53; 955; 957; 958; 961. 

116 The flying circus of physics 


Oasis mirage 

What causes the water mirage com- 
monly seen on hot streets? What 
features partially convince you that 
there is water in the street? Also, 
why do there seem to be palm 
trees around oasis mirages (even 
in areas where such trees cannot 
grow)? To a thirsty man, of course, 
the palm trees are more than 
enough to convince him of a 
water supply (Figure 5.9). 

A pelican discovered on a hot 
asphalt highway in the midwest 
might have almost met its end 
because of the water mirage. 

The miserable bird had 

obviously been flying, 

maybe for hours, across 

dry wheat stubble and 
had suddenly spotted 
what he thought was 
a long black river, thin 
but wet, right in the 
midst of the prairie. 
He had put down for 
a cooling swim and 
knocked himself 

Did the bird see a mirage? 
165, pp. 164-165; 170, 
pp. 391-392; 219, pp. 
295-296; 533, pp. 75-76; 
954, pp. 45-46; 955 
through 957. 

*C. A. Goodrum, The New Yorker , 

38(8), 115 (1962). 


Figure 5.9 

Mirage. (By permission of John Hart. Field Enterprises.) 

Minnaert (954) describes a 
multiple image mirage that can be 
seen along a reasonably long wall 
facing the sun. (He suggests a 
length of 10 yards or more.) Place 
your hand against the wall and 
watch a bright metal object a friend 
brings near the other end of the 
wall (Figure 5.10). When the object 
is a few inches from the wall, it will 
appear distorted and you will see a 
reflected image in the wall as 
though the wall were a mirror. On 
a very hot day you may even see a 
second image as well. Why is there 
an image of the object inside the 

954, pp. 43-44. 

She comes in colors everywhere 117 




Figure 5.11 


Paper doll mirage 

A different type of mirage, the 
"superior mirage," involves one or 
more images of an object as shown 

in Figure 5.11. What's responsible 
for those images? 

164, pp. 470-473; 165, p. 164; 
954, p. 51; 955; 958. 


One-way mirrors 

One way mirrors are used a lot 
in spy movies, but are they 
really one-way! Try to devise 
a glass or a glass coating so that 
room scenes will pass in only one 
direction. If this is impossible, 
then how do the so-called one- 
way mirrors work? 



Red moon during lunar eclipse 

Why is the moon red during a 
lunar eclipse— that is, when the 
moon is in the earth's shadow? 

954, pp. 295-296; 983, pp. 


Ghost mirage 

There are, or course, many curious 
stories of strange mirages. Can you 
explain the following one? 
One hot August afternoon 
a woman was picking 
flowers from the wet ground 
when . . .she suddenly per- 
ceived a figure at the dis- 
tance of a few yards from 
her. It was standing on a 
wet spot where there was 
a little thin mist (possibly 
steam) rising, and wavered 
a little, never remaining 
still, though she says, 
'it had a great deal of 
bulk.' It was on a level 
with herself and formed 
a species of triangle, with 
herself and the sun. She 
was looking towards the 
sun, but not directly to it. 
She thought at first that 
the figure might be a delu- 
sion: it stood exactly 
facing her and she first 
discovered it to be her 
own image by perceiving 
that like herself, it held. . . 
a bunch of flowers. She 
moved her hand with its 
nosegay and the figure 
did the same. The dress 
and flowers were precisely 
similar to her own and the 
colours as vivid as the 
reality. She could see the 
colouring and the flesh: it was 

118 The flying circus of physics 

like looking at herself in 

a looking-glass (962). 
Needless to say, this soon unnerved 
the woman, and "she fled down 
the steep hillside, often stumbling, 
to rejoin her friends, both of 
whom had seen the figure" (962). 


Figure 5.15 

How many "y oil's" do you see? 


Number of images in two mirrors 

How many images of yourself do 
you see while standing in front of 
two adjacent plane mirrors such 
as you find at a clothing store 
(Figure 5.15)? How does the 
number of images depend on the 
angle between the mirrors? Does 
it matter where you stand? If it 
does, where do you stand to see 
the most images? Are your 
answers the same for the number 
of images you will see of a pack- 
age lying next to you? 

985 through 989; 1524. 


The green flash 

Just as the top of the setting sun 
disappears beneath a clear, flat 
horizon, you may be able to see, 
for 10 seconds or so, a distinct 
green flash from the sun. Why 
does this happen? Could it be 
an optical illusion (say, an 
afterimage of the sun)? This was 
the common opinion for a long 
time, until photographs were 
made of the flash.* 

In higher latitudes it can be seen 
for longer times "Members of 
Byrd's expedition to the South 
Pole are reported to have seen it 
for 35 minutes while the sun, rising 
at the close of the long winter 
night, was seen to be moving almost 
exactly along the horizon" (978). 

Clear horizons, such as over the 
Pacific, are a definite asset. "Ac- 
cording to Rear Admiral Kindell, 
strong and brilliant flashes were 
seen by him and other members 
of the U.S. Navy during the 
Okinawa campaign of 1945 at 
almost every sunset on clear days" 

A similar effect, although very 
rare, is the red flash that may ap- 
pear when the sun peaks out 
beneath a cloud. 

164, pp. 58-63; 165 f p. 160; 
362 f pp. 152-153; 966 
through 981; 1614. 

*0'Connell's book (966) is full of green 
flash photographs. 

\ Unmixed sugar in waters 


Figure 5.17 

Laser beam bouncing in a sugar 
solution. [After W. M. Strouse, 
Am. J. Phys., 40, 913 (1972).] 


Bouncing a light beam 

If a narrow light beam (such as a 
laser beam) enters a container of 
water in which several lumps of 
sugar have been added without 
stirring, the light beam will bend 
and then bounce off the bottom 
as shown in Figure 5.17. What 

makes the beam bend down? 
What makes it bounce? And final- 
ly, once it is going up, what makes 
it bend down again? 

963; 1551. 

She comes in colors everywhere 119 


Flattened sun and moon 

What causes the apparent flattening 
of the sun and moon when they are 
near the horizon? Can you roughly 
calculate the amount of distortion? 

164, p. 470; 219, pp. 297-298; 
954, pp. 39-40; 964; 965. 



3rewster angle 


Blue ribbon on sea horizon 

The horizon on the sea often ap- 
pears to be a much darker blue or 
gray than the sky or the rest of 
the sea. In fact, if you're standing 
on a beach, it almost appears that 
someone has stretched out a bright 
blue ribbon to mark the horizon. 
The ribbon disappears, however, 
if you lie on the beach or if you 
climb to a greater height. One 
clue about what causes the rib- 
bon might be that the light from 
it is almost completely linearly 
polarized. Can you explain the 
ribbon and the polarization? 



30° reflection off the sea 

If you look at the sea just below 
the horizon, you will see reflections 
of objects that are more than 30° 

above the horizon. Objects less 
than 30° above the horizon are not 
reflected. Why? Is the minimum 
reflection angle determined by the 
average wave slope that, because 
of your observations, must be 
about 15°? Actually, it is not. 
Can you think of any other reason 
why the reflection is restricted in 
this way? 

954, pp. 23-25; 990. 


Lunar light triangles 

When the moon is reflected in the 
sea or a lake, why is there a lumin- 
ous triangle on the surface of the 
water (Figure 5.21)? What deter- 
mines the shape and width of the 
luminous area? Why is there a 
corresponding dark triangle in 
the sky above the water? 

399, pp. 243-246; 954, pp. 
23-27, 138-139; 991; 992, 
pp. 74-80. 

Figure 5.21 

Lunar light triangle in the water 

and a dark triangle in the sky. 

By permission of John Hart 
Field Enterprises. 


Shiny black cloth 

Why do some types of cloth 
glisten while others do not? 
Black felt has a shiny side and 
a dull side. Some wall paints are 
glossy black; others are flat 
black. Since black absorbs visible 
light, how can a black surface be 

253, pp. 278-279; 533, pp. 33- 

1 20 The flying circus of physics 

pinhole optics 


Inverted shadows 

Punch a pinhole in an opaque sheet 
of paper, hold the paper a few 
inches from one eye, close the 
other eye, and then carefully hold a 
thin nail between the pinhole and 
you (Figure 5.23a). Move the nail 
around until a shadowy figure ap- 
pears in the circle of light from the 
pinhole (Figure 5.23b). What causes 
that figure, and why is it inverted 
from the nail? Also, why does the 
figure appear to be on the far side 
of the pinhole? 

533, pp. 49-51; 993; 1582. 

Figure 5.23a 

Hold a thin nail between your 

eye and a pinhole. 

Figure 5.23b 

Shadowy image of the nail in the 

pinhole image. 

ray optics 






Pinhole camera 

The simplest type of camera, and 
the easiest to build, is the pinhole 
camera. Moreover, there are some 
definite advantages to using a 
pinhole instead of a lens. For 
example, there is no linear dis- 
tortion, and there is tremendous 
depth of field. Are there aber- 
rations of any significance? In 
particular, is there any chromatic 
distortion in a simple pinhole 
camera? Finally, what is the best 
hole size, and what happens to 
your pictures if the hole is larger 
or smaller than the best size? 

994 through 998; 1501 
through 1503; 1586. 


Eclipse leaf shadows 

If you look at the shadows of 
leaves during a solar eclipse, you 
will see images of the eclipsing 
sun projected onto the ground. 
Why are these images made? Are 
they present all the time or just 
during an eclipse? 

360 \ pp. 66-67; 533, pp. 29- 
31; 999. 



Some morning when the grass is 
sparkling with dew, look at the 
shadow of your head on the 
grass. Around the shadow will be 
a bright light called the heiligens- 
chein. How, exactly, does the 
dew cause this brightening, and 
why isn't there heiligenschein 
around your entire shadow? Do 
the blades of grass play any part 
in the effect besides holding up 
the dewdrops? Can you also 
explain the very bright heili- 
genschein that astronauts see when 
walking on the moon? (It certainly 
isn't due to dew-covered grass.) 

164, p. 556; 165, p. 180; 360, 
p. 68; 362, pp. 136-137; 380; 
954, pp. 230-234; 983, Chapter 
2; 1000 through 1008. 


Bike reflectors 

If you shine light on a bike reflec- 
tor at virtually any angle, the light 
will be reflected back to the source 
Why is the reflector so good at 
this? An ordinary mirror will re- 
flect well, of course, but it will 
not return the light to the source 
unless the incident light is per- 
pendicular to the surface. What, 
then, is different about the bike 
reflector? If a narrow beam of 
light is reflected by a bike 
reflector, how wide will the 
return beam be? 

170, p. 158; 1011. 

She conies in colors everywhere 121 


Brown spots on leaves 

It is a bad idea to sprinkle water on 
tree leaves during the day, because 
the water drops leave brown spots 
on the leaves. What causes the 


Rays around your head's shadow 

I looked at the fine centri- 
fugal spokes round the 
shape of my head in the 
sunlit water. . . Diverge, 
fine spokes of light from 
the shape of my head, or 
anyone's head, in the sun- 
lit water! ---Walt Whitman, 
"Crossing Brooklyn Ferry", 
Leaves of Grass 

These rays of light surround the 
shadow of your head if the shadow 
is cast upon slightly turbulent 
water. If the water is calm or has 
regular waves, the rays do not 
appear. Why? 

954, pp. 333-334; 1009; 1010. 


Cats' eyes in the dark 

Why do a cat's eyes shine so 
brightly in the dark when you 
illuminate them with a flash- 
light? Why aren't they so notice- 
ably bright during the day? Does 
the amount of reflection depend 
on the angle between your line of 

sight and the incident light beam? 
Why don't our eyes shine as much 
when illuminated at night or 
with a flashbulb? 

954, p. 350; 983, p. 36; 1012. 


Brightness of falling rain 

Occasionally you can see distant 
rain falling, and in some case you 
may notice that "when these 
regions of falling precipitation are 
illuminated by direct sunlight, a 
distinct horizontal line can be 
seen, above which the precipita- 
tion appears much lighter than 
below" (1013). What is responsible 
for the change in brightness? 



Rainbow colors 

The color separation in the 
primary rainbow is usually ex- 
plained as simple refraction and 
reflection of the light rays with- 
in raindrops. However, since the 
light rays are incident on a drop's 
surface within a wide range of 
angles to that surface (Figure 
5.32), shouldn't the emerging 
light rays, even those of a 
particular color, also leave the 
drop in a wide range of angles? 
Why, then, do you see a parti- 
cular color subtending a par- 
ticular angle from the rainbow? 

As a matter of fact, are rainbow 
colors actually as pure as a prism's? 
If the simple refraction explanation 
is correct, shouldn't the rainbow 
have pure colors? 

Figure 5. 32 

Light rays from sun incident on a 

water drop. 

Why is the color sequence in 
the secondary rainbow opposite 
that in the primary rainbow, and 
why is the secondary rainbow so 
seldom seen? As a matter of fact, 
why can only two rainbows be 
seen in the sky? If the primary 
rainbow is due to a single reflection 
of light rays inside the raindrops, 
and the secondary rainbow is due 
to a double reflection, should not 
there be more rainbows resulting 
from further internal reflections? 

A double rainbow can also be 
seen in the beam of a searchlight 
during a light rain at night. As the 
beam sweeps through the sky, the 
rainbows slide up and down the 
beam and may even disappear 
briefly. Can you account for 
such motion of the rainbows? 

164, Chapter 3; 165, p. 177; 
380; 954, pp. 174-179; 983, 
Chapter 3; 1014, Chapter 13; 
1015 through 1021; 1499; 
1627 through 1631. 

1 22 The flying circus of physics 


Pure reds in rainbows 

Why can pure reds be found only 
in the vertical portions of rainbows 
when the sun is relatively low?* 
(The sun must be low so that the 
vertical portions of the rainbows 
can be seen; if you are viewing 
the rainbow from a high point, 
the sun will not have to be so low.) 


*Even the most commonplace features 
of the outside world still afford fresh 
understandings and surprises. Fraser 
(1022) points out that this simple fea- 
ture of pure reds being restricted to 
the vertical portions of the rainbow some- 
how escaped notice until his paper of 
1972. As another example of modern 
work, it has only been recently that 
photographs of the infrared rainbow 
have been taken (1023, 1024), thus 
allowing man to see for the first time 
what has periodically hung in the sky 
for millions of years. 


Supernumerary bows 

Sometimes several pink and green 
bows can be seen below and adja- 
cent to the primary bow. Very 
rarely they can also be found 
above the secondary bow. What 
causes these additional bows? 
Don't they come as a surprise 
if you draw too simple a picture 
of the rainbow? Why aren't they 
found between the primary and 
secondary bows? 

164, pp. 477, 483; 954, p. 
178; 983, Chapter 6; 1014, 
pp. 241-242; 1019 through 
1021; 1025. 


Dark sky between bows 

Why is the region of sky between 
the primary and secondary rain- 
bows darker than the rest of the 

164, pp. 482-483; 954, pp. 179- 
180; 983, p. 56; 1020. 


Rainbow polarization 

Is the rainbow polarized? If it is, 
can you explain its polarization? 

361, pp. 8-9; 954, pp. 181-182; 
983, pp. 59 ff; 1014; 1020; 1630. 


Lunar rainbows 

Lunar rainbows are very rare. Is 
this only because moonlight is 
so much dimmer than sunlight, 
or is there some other reason? 

164, p. 476; 954, p. 189; 1020; 
1026; 1027. 


Rainbow distance 

How far away from you are rain- 
bows formed? That is, how dis- 
tant are the water drops? Is 
it possible to have a rainbow a 
few yards away from you? 

If you look at a rainbow in your 
garden sprinkler, you may very well 

see two bows crossing over each 
other (Figure 5.38). Why? 

164, p. 496; 954, pp. 169, 174; 

Figure 5.38 

Rainbows seen in water-sprinkler 



Rainbow pillar 

What causes the very rare pillar 
of light that has been seen at the 
foot of some rainbows (Figure 
5.39)? [Minnaert (991 ) gives a 
photograph of such a pillar, along 
with the comment that these pillars 
have not yet been explained.] 

991; 1028, plate 24; 1029. 

Figure 5.39 

Rainbow pillar at the foot of a 


She comes in colors everywhere 123 

Figure 5.40 


Reflected rainbows 

If you ever get a chance to see 
both a rainbow and its reflection 
in water, you'll notice they are 
different in shape and position. 
If a cloud is present, for example, 
you may see something resembling 
Figure 5. 40 . Why is there a dif- 
ference in the cloud's position rela- 
tive to the rainbow? 

164, pp. 497-499; 165, p. 175; 
954, pp. 186- 187; 983, p. 68; 
1020, pp. 272-275. 

Figure 5.41a 

Dew bow in grassy field. 



What causes the rainbows seen 
on dew-covered grass fields 
(dewbows) and on ponds with 
oily surfaces? In particular, can 
you explain their shape (Figure 
5.41a)? Why do dewbows formed 

Figure 5.41b 

Dewbows as seen by someone 

under a street light at night. 

(After J. O. Mattsson, S. Nord- 

beck, and B. Rystedt, Ref. 


by streetlights have yet another 
shape (Figure 5.41/?)? 

164, pp. 499-500; 165, pp. 175- 
176; 954, pp. 184-186; 1020; 
1030; 1031. 


Sun dogs 

Sun dogs (mock suns or parhelia) 
are bright images of the sun 
that sit to one or both sides of the 
sun. They are normally outside 
the 22° halo (if the halo is visible), 
as shown in Figure 5.43, being 
further away the higher the sun is 
in the sky. When the sun is higher 
than 60° , however, the sun dogs 
disappear. Can you explain 
what produces the sun dogs and 
why their position and existence 
depend on the sun's height? Also, 
why are they so much more color- 
ful than the 22° halo? 

164, pp. 510 ff; 165, pp. 169- 
171; 361, pp. 24-25; 362, 
pp. 1 40 ff; 380; 954, pp. 196- 
197; 983, pp. 70-73, 84 ff; 
991; 1044 through 1051. 

1 24 The flying circus of physics 


The 22° halo 

Halos around the moon and sun 
are fairly common in most areas. 
The primary halo is 22° from the 
sun or moon (Figure 5.43) and is 
colored red on the inside and 
white or blue on the outside. 
Except for the corona immediately 
surrounding the sun or moon, 
the sky inside the 22° halo is 

Certainly the halo is caused by 
scattering of the light somewhere 
in the atmosphere, but what kind 
of scattering could give such a uni- 
form design? For example, would 

you expect to get a 22 halo from 
sunlight scattered by high altitude 
dust? Also, why is the area within 
the halo dark? 

Almost universally the halo has 
been thought to be a sign of im- 
minent rain. Is there any truth 
to that belief? 

164, pp. 512-513; 165, pp. 169- 
174; 219, pp. 298-299; 360, pp. 
78-79; 361, pp. 24-25; 362, pp. 
140-143; 954, pp. 190-195; 
983, Chapter 4; 991; 1033 
through 1050; 1610. 

22* halo 


Sun dog 


Figure 5.43 

The 22 halo and sun dogs around the , 



Why are fogbows-rainbows formed 
in the fog -whitish bands with 
orange on the outside and blue 
on the inside? Why are they about 

twice as wide as normal rainbows? 

Can fogbows be produced by 
streetlights? If so, what difference 
do you expect from the fogbows 
formed in sunlight? 

165, p. 175; 380; 954, p. 183; 
1020; 1030; 1032; 1628. 

Figure 5.45 


Sun pillars 

Pillars of sunlight above and below 
the sun (Figure 5.45) can be seen 
fairly often near sunset or after 
sunrise. The columns may be 
white, pale yellow, orange, or pink, 
so they are quite pretty. Under 
some conditions they can even 
be seen above and below outdoor 
artificial lights such as streetlights. 
What causes these pillars? 

164, pp. 543-544; 165, pp. 169, 

172; 361, pp. 32-33; 362, pp. 

148- 149; 954, pp. 20 1-202; 983, 
pp. 135 ff; 1028, plate 23, p. 
245; 1033; 1035; 1065; 1066; 


She comes in colors everywhere 125 

■ ■ . ■ --»— 

(a) 22° halo, (b) Sun dogs to 

p .-■ p ' 

22° halo, (c) 46° halo, (d) 

Circumzenith arc. (e) Parhelic 

" o 

circle, (f) Sun dogs to 46 halo. 

(g) Parry arc. (h) Supralateral 

tangent arcs to 46 halo, (i) 

Tangent arcs to 22 halo, (j) 

m m 

Lowitz arcs, (k) Infralateral 

I I 

tangent arcs to 46 halo. (1) 

Paranthelia. (m) Paranthelic arcs. 

(n) Narrow -angle oblique arcs to 

anthelion. (o) Anthelion. (p) 

Wide-angle oblique arcs of anthe- 


e P Zenith p e 

■ d 

f l l f 

b a b 

~ a h 

k J- Sun ^ k 

Figure 5.46 

Some of the possible arcs, halos, and sun dogs around the sun. 

(Not all can be visible simultaneously.) 


Other arcs and halos 

The full array of possible arcs and example, has apparently only 

164, Chapters 4, 5; 165, pp. 169- 

halos could be awesome if all of recently been explained (1058). 

174; 361, pp. 28-29; 362, pp. 

them were visible at once. (See Several of the arcs can change 

140- 149; 380; 954, pp. 190- 

Figure 5.46.) Usually, however, shapes tremendously as the sun 

206; 983, Chapter 4; 991; 1034 

you will see only a few arcs or changes height, so it pays to 

through 1038; 1044 through 

halos. Some are so rare, in fact, watch as long as possible, making 

1064; 1514; 1515; 1622. 

that their existence is still con- occasional sketches. See if you 

troversial. The Lowitz arc, for can explain the ones you do find. 

126 The flying circus of physics 

electric field 



Crown flash 

Concurrent with a lightning stroke 
in the main body of a storm cloud, 
there may be a brightening that 
ripples upward and outward through 
the top of the cloud. Is this 
brightening (called "crown flash" 
and "flachenblitz") an unusual 
type of discharge, or is it a peculiar 
reflection of light from the initial 
lightning stroke? 

301, pp. 50-51; 1067 through 


(5.48 through 5.57) 


Polarization for car lights 

Polarized plastic sheets were first 
developed to cover car headlights 
so as to reduce the glare of an ap- 
proaching car at night. How 
could this be accomplished, and 
what would be the best orienta- 
tion of the polarized sheets? 
Don't forget that you still want 
to see the oncoming car, so the 
light shouldn't be entirely 
blocked out. Will the tilt of 
the windshield matter? Could 
you obtain similar results with 
polarized sunglasses? 

1070, pp. 111-114; 1071 
through 1074. 


Polarized glasses and glare 

Why do polarized sunglasses reduce 
glare? (Unpolarized sunglasses just 
decrease the total amount of light 
entering your eyes and do not pre- 
ferentially block the glare.) When 
will polarized sunglasses improve 
a fisherman's ability to see beneath 
the water? 

1070, pp. 100-102. 


Sky polarization 

Why is the light coming from a 
clear sky polarized? Where should 
the region of maximum polariza- 
tion be? Can you verify your 
prediction by using a pair of 
polarized sunglasses? Is light from 
clouds polarized? Why are some 
areas of the sky unpolarized? 
Why is the polarization in some 
parts of the sky perpendicular 
to that predicted by conventional 
theory? Can you also find these 
neutral points and areas of per- 
pendicular polarization with 
your sunglasses? 

164, pp. 571-575; 165, pp. 194- 
204; 170, pp. 4 13-4 14; 360, pp. 
62-63; 362, pp. 152-153; 446, 
pp. 43-45; 533, pp. 193-196; 
954, pp. 251-254; 1070, pp. 98- 
99; 1075, pp. 12-17; 1076 
through 1079. 


Colored frost flowers 

Some morning after a cold night, 
examine the thin, transparent 
frost flowers on a window facing 
the sun. If the flowers have 
started to melt and have formed 
a pool of water at the bottom 
of the window pane, look for 
reflections of the flowers in the 
pool (Figure 5.51). They will 
appear as patterns of colored 
fringes. What causes the color 
in these reflections? 


Pool of 
melted water 

Figure 5.51 

Optics for seeing frost flowers. 
[After S. G. Cornford, Weather, 
23, 39 (1968). 


Cellophane between two polarizing 

Light will not pass through two 
polarized sheets whose polariza- 
tion directions are perpendicular. 
But if clear cellophane is inserted 

She comes in colors everywhere 127 

between them, light is transmitted, 
the amount of transmission depend- 
ing on the cellophane's orientation. 
If you replace the cellophane with 
a piece of plastic food wrap you will 
find that very little light is trans- 
mitted. By stretching the food 
wrap, however, you can once 
again get a large transmission. What 
is the fundamental difference 
between cellophane and un- 
stretched food wrap that ac- 
counts for the difference in 
transmission? How are the op- 
tical properties of the food wrap 
changed by stretching?* 

170, pp. 420 ff; 360, pp. 14- 
16; 1077; 1078; 1081; 1082, 
pp. 79-93. 

*For a whole bagful of optical devices 
and tricks that can be made with cello- 
phane, tape, etc., see Chapters 8 and 9 
of Crawford's excellent book Waves 
(170). Also see Refs. 1096 and 1097. 


Spots on rear window 

If you wear polarized sun glasses 
while driving, you have probably 
noticed the large spots, usually 
arranged in patterns, on the 
rear windows of other cars. What 
are those spots, and why must 
you wear the polarized sunglasses 
to see them? Are the spots 

360, pp. 14-16. 


Light source 

Polarizing Syrup 



Figure 5.54 

Detection of polarization change by syrup. 


Optical activity of Karo syrup 

Although you probably have 
used Karo corn syrup on your 
pancakes, you most likely are 
unaware of the syrup's most 
fascinating property : its optical 
activity. Try this experiment; 
between two polarizing filters 
(they can be from polarized 
sunglasses), put a glass of Karo 
syrup. Then place a white light 
source on one side of the glass 
and look at the light through 
the syrup (Figure 5.54). What is 
responsible for the beautiful colors 
you see? By turning one of the 
filters (while leaving the other 
fixed), find the polarization of the 
emerging light and thus the 

polarization change experienced 
by the light in the syrup. By re- 
peating this procedure for several 
thicknesses of syrup, you will 
discover that the polarization 
change depends on the distance 
the light travels through the syrup. 
Why? How much rotation of the 
polarization is there per centimeter 
of syrup, and is it clockwise or 
counterclockwise? Why is the rota- 
tion in one direction instead of 
the other? 

155, p. 425; 170, pp. 425-426, 
447; 533, p. 198; 1070, pp. 
115-118; 1082, pp. 136-144; 
1083; 1084. 


Animal navigation by polarized 

Honeybees, ants, and various other And how can they use this ability 

creatures use the polarization of 
the sky* as an aid to navigation. 
How are they able to detect the 
polarization angle of the light? 

*See Prob. 5.50. 

to navigate? 

332, Vol. I, p. 36-7; 1070, 
p. 98; 1085, Chapter 13; 1086 
through 1089; 1557; 1584. 

1 28 The flying circus of physics 


Magic sun stones 

Dichroic crystals are different 
colors when under light of dif- 
ferent polarizations. The crystal 
may be clear with a faint yellow 
tinge under light of one polariza- 
tion, but dark blue when the 
polarization is changed by 90°. 

It is believed that the Vikings 
used a dichroic crystal (cordierite) 
to locate the sun when it was not 
directly visible. At least, accord- 
ing to the tales, they had some 
kind of magic "sun stone" by 
which they could find the sun 
even when it was behind the 
clouds or below the horizon. 
Since in the high latitudes the 
sun can be below the horizon 
even at noon, such magic stones 
would have been a very valuable 
navigational aid. 

Why are different colors 
transmitted through such crystals 
for different incident polarizations? 
Can the cyrstals really be used to 
find the sun even if the sky is 
cloudy or the sun is below the 

170, pp. 448-449. 


Haidinger's brush 

You may not realize it, but you 
are capable of detecting polarized 
light with your own eyes. By 
looking through a polarizing sheet 
(polarized sunglasses, for example) 
at a bright light, you will momen- 
tarily see a yellow hourglass figure 
with a blue cloud to each side 






Figure 5.57 

(Figure 5.57). Suddenly rotating 
the filter in its own plane may 
help you to spot the hourglass 
easier. This pattern is called 
Haidinger's brush and is a direct 
result of the linear polarization 
caused by the filter. But why? 
What part of the eye is sensitive 
to the polarization sense, and 
why is this particular pattern 
created? How does the orientation 
of the hourglass depend on the 
polarization axis? Why does the 
pattern fade after a few seconds? 
I can see the brush fairly well, 
without a polarizing filter, in 
the partially polarized light of 
the sky. Some people see it so 
clearly that it becomes irritating. 
You can also detect circularly 
polarized light with your eyes: 
left-circularly polarized light 
gives a yellow brush tilted to 
the right at about 45°, whereas 
the opposite polarization gives 
a brush titlted to the left at about 
45°. Why? 

954, pp. 254-257; 1070, pp. 
95-97; 1090, pp. 300-304; 
1091, Vol. 2, pp. 304-307; 
1092 through 1094; 1621. 


(5.58 through 5.90) 

Rayleigh and Mie scattering 




Sunset colors 

All of us too often neglect sunsets, 
especially physicists who tend to 
shove the twilight colors under the 
heading of "Rayleigh scattering" 
and then forget them. Can you 
explain the beautiful variety of 
colors in the twilight sky? (The 
setting sun may be red, but the 
sky is certainly not just red.) As 
the sun sets, the western sky first 
assumes yellow and orange tints. 
By the time the sun has turned 
a fiery red, the afterglow left in 
the western sky varies upward from 
the horizon from a yellow-orange 
to a green-azure. Eventually the 
area about 25° above the western 
horizon turns rose-colored (the 
"purple light" discussed below). 

Especially brilliant twilight 
colors can be seen soon after major 
volcanic eruptions. What causes 
such color enhancements? 

164, pp. 566-567; 165, pp. 
184 ff; 380; 954, Chapter 1 1; 
983, pp. 234-244; 1075; 1102 
through 1 109; 1526. 

She comes in colors everywhere 129 


The blue sky 

Probably the all-time standard 
physics question is "Why is the 
sky blue?" Physicists often toss 
it aside with a few mutterings 
about "Rayleigh scattering." 
Certainly the question deserves 
better treatment than that. For 
example, what part of the sky 
is bluest, and why isn't the entire 
sky a uniform color? Does the 
daytime sky color actually follow 
the Rayleigh prediction? Why 
isn't the sky blue on nights with 
a full moon? What is scattering 
the sunlight to produce the day- 
time sky color? Would you get 
a blue sky if the scatterers were 
much larger or much smaller? 
Finally, why is the sky on Mars 
blue only within a few degrees 
of the horizon, and black over- 

164, Chapter 7; 165, pp. 192 ff; 
170, pp. 559-562; 466, pp. 35 ff; 
954, pp. 238-251; 983, Chapter 
9; 1075, p. 10; 1079; 1098 
through 1 102; 1505; 1526. 


Twilight purple light 

What causes the purple light (which 
may be more pink than purple) 
that first appears in the western 
sky as the sun sinks beneath the 
horizon (Figure 5.60)? It is the 
brightest about 15 to 40 minutes 
after sunset. 

Is the same physics responsible 
for the "second" purple light that 
sometimes appears after the com- 
mon one has vanished and which 



, ~ Sun 
Qs below 

Figure 5. 60 

Sunset phenomena. (After 
H. Neuberger, Introduction to 
Physical Meteorology, Pennsy- 
lvania State University.) 

may last up to two hours after 
sunset? How could the sun still 
provide light to the sky after 
having set an hour or so earlier? 

164, p. 567; 165, pp. 184-192; 
954, pp. 270-280; 1075; 1 102; 
1104; 1110. 


Zenith blue enhancement 

Have you ever noticed the zenith 
(overhead sky) turns a deep blue 
during sunset (Figure 5.60)? Isn't 
that strange? Wouldn't you think 
the zenith would be red, for the 
same reason the setting sun is red? 

466, pp. 207-208; 1075, 
Chapter 4; 1102. 


Belt of Venus 

What causes the twilight's rosy 
patch ("belt of Venus") that 
borders the earth's shadow as the 
shadow rises out of the east 
(Figure 5.60)? 

164, p. 566; 165, pp. 184 ff; 
954, pp. 268 ff; 1075. 


Green street lights and red 
Christmas trees 

While flying into a city you may 
have noticed that many streets 
are lit by green lights. When you 
drive through these streets, how- 
ever, the lights are not green at all, 
but white. Why is there a color 
difference in the two situations? 
Similarly, why is the light from a 
distant Christmas tree primarily 
red when in fact the tree is 
covered with lights of many 

11 11, pp. 172-173; 1112. 


Brightness of daytime sky 

Why is the daytime sky bright? 
Can you calculate roughly how 
bright it is? 

164, pp. 563-565; 170, pp. 559- 
562; 466, pp. 35 ff; 954, pp. 
245-247; 1075; 1 100, p. 33. 

1 30 The flying circus of physics 


Yellow ski goggles 

Although skiers wear yellow- 
tinted goggles largely to be 
fashionable, they often claim 
that the goggles improve their 
vision on hazy days. Supposedly, 
a skiier can better distinguish the 
small snow bumps in his path. 
Such a claim must have some 
validity, because the famous polar 
explorer Vilhjalmur Stefansson also 
recommended amber glasses for 
travel across snow and ice fields. 
Why might yellow glasses help? 
For example, is there a dominance 
of yellow in snow-reflected sun- 
light on hazy days? 

354; 1113, pp. 200-202. 


Stars seen through shafts 

Ever since Aristotle men have 
believed that stars can be seen 
in the daytime if they are 
viewed through long shafts such 
as chimneys. A shaft will 
decrease the total skylight seen, 
thereby (supposedly) allowing the 
stars to be distinguished in the 
small patch of light at the top of 
the shaft. Your partial dark adap- 
tation (due to the smaller amount 
of skylight you see) may also aid 
in the distinction. Do you believe 
such measures will actually make 
stars visible in the daytime? Can 
you verify your belief by calcula- 
tions and by trying the experiment? 

/ / 14; 1 1 15. 





Colors of lakes and oceans 

What is the color of a clear, clean 
mountain lake? Does it matter if 
the sky is clear or cloudy? How 
much do the material on the bot- 
tom and the depth of the water 
matter? What is responsible for 
the different colors of other 
lakes? What color is the ocean 
near the shore and far at sea? 
What colors do you see in ocean 

While swimming as deep as pos- 
sible, hold out a hand horizontally 
and notice that the top is a differ- 
ent color than the bottom. Why 
is there a color difference? 

360, pp. 17- 19; 380; 466, pp. 
201-203; 954, pp. 308-335; 
992, Chapter 13; 1116 through 





Color of overcast sky 

If you have ever lived in the 
country, you may have noticed 
a seasonal change in the color of 
an overcast sky. Some people 
claim that an overcast sky is 
slightly greener in the summer than 
in the winter. Now I could make 

the obvious guess about what causes 
this color change, if it really does 
happen, but is there any validity 
to my guess? 

1 1 19. 


Seeing the dark part of the moon 

When the sun has just set and the 
new moon appears as a narrow 
crescent, the "dark" part of the 
moon can be seen. How is that 

466, p. 199; 954, p. 297. 


White clouds 

Why are most clouds white? Why 
aren't they blue like the sky? 
Why are thunderclouds dark? 

332, Vol. I, p. 32-8; 1 123; 


Sunlight scattered by clouds 

Why does water scatter so much 
more sunlight after it has con- 
densed to form clouds than before, 
when it was just water vapor? Isn't 
the total number of atoms the 
same, and shouldn't the scattered 
light thus be the same? 

332, Vol. I, p. 32-8; 1123. 

She comes in colors everywhere 131 

Figure 5. 72 

A kayaker finding his way 
through the ice field by the map 
in the sky. 


Maps in the sky 

Over the ice fields in the far north, 
large maps of the surrounding re- 
gion sometimes appear at the 
base of overhanging clouds. These 
maps, called "ice blink" and 
"cloud maps," allow the Eskimo 
to pick a route through the ice 
field if he is kayaking, or over 
the ice if he is sledding (Figure 

On approaching a pack, 

field, or other compact 

aggregation of ice, the 

phenomenon of the ice- 
blink is seen whenever 

the horizon is tolerably 

free from clouds, and 

in some cases even 

under a thick sky. The 

"ice-blink" consists in 

a stratum of a lucid 
whiteness, which ap- 
pears over ice in that 
part of the atmosphere 
adjoining the horizon. . . 
when the ice-blink oc- 
curs under the most 
favorable circumstances, 
it affords to the eye a 
beautiful and perfect map 
of the ice, twenty or thirty 
miles beyond the limit 
of direct vision, but less 
distant in proportion as 
the atmosphere is more 
dense and obscure. The 
ice-blink not only shows 
the figure of the ice, but 
enables the experienced 
observer to judge 

whether the ice thus 
pictured be field or packed 
ice; if the latter, whether 
it be compact or open, 
bay or heavy ice. Field- 
ice affords the most lucid 
blink, accompanied with 
a tinge of yellow; that of 
packs is more purely 
white; and of bay -ice, 
greyish. The land, on 
account of its snowy cover- 
ing, likewise occasions a 
blink, which is more yellow 
than that produced by the 
ice of fields (1120). 
Can you explain these cloud maps? 

1075, p. 8; 1 1 13, p. 220; 1 120 
through 1122. 

132 The flying circus of physics 

Mother-of-pearl clouds 


Not all clouds are white or dark. 
Mother-of-pearl clouds (nacreous 
clouds) may have very beautiful, 
delicate colors. Though they are 
rare and are usually seen only in 
the high latitudes and only after 
sunset, they can occasionally 
he bright enough to color snow 
on the ground. What is different 
about these clouds so that they 
show such colors? Do the colors 
arise from a fortuitous particle 
size? Why are these clouds usually 
confined to the high latitudes and 
to an altitude range of about 20 
to 30 kilometers? 

361, pp. 20-21, 28-29; 362, 
pp. 74-75; 536, p. 170; 954, 
pp. 229-230; 1 124 through 
1 129. 



Young's dusty mirror 

When you look past a small lamp 
directly into a dusty mirror, 
you will find that the reflected 
image of the lamp is surrounded 
by distinct colored fringes. A 
very clean mirror won't make the 
fringes; you must have a dusty 
or slightly dirty one. What causes 
the fringes, and how many fringes 
of any one color are there? 
Most of all, why must the mirror be 
dusty or slightly dirty? 

1130; 1131. 




Sudden end 
to beam 

Figure 5. 75 


Searchlight beams 

Why do searchlight beams (the kind 
used for airplane detection in 
World War II but that have now been 
demoted to signaling supermarket 
openings) end as abruptly as they 


Zodiacal light and gegenschein 

The next time you find yourself 
away from city lights on a clear 
moonless night, search for the 
zodiacal light and gegenschein. The 
former is a milky triangle that may 
be in the west for a few hours 
after sunset or in the east before 
sunrise. The triangle is nearly as 
bright as the Milky Way and is 
oriented along the plane of the 

do (Figure 5.75)? Wouldn't you 
expect a gradual fading of the 

954, pp. 262-263; 1 147. 

ecliptic* The gegenschein is a 
rather faint light seen at the an- 
tisolar point in the sky. What is 
responsible for these lights in the 
night sky? 

954, pp. 290-295; 1 143 through 

*The ecliptic plane is the plane in which 
the earth orbits about the sun. 

She comes in colors everywhere 133 


Figure 5.77 

Streak of light in windshield from streetlight 


Windshield light streaks 

When driving through rain at 
night you will find long streaks 
of light on your front windshield 
due to the lights outside your 
car (Figure 5.77). Each streak ap- 
pears to run through the lights 
source, and the smaller sources 
(such as streetlights) give more 
pronounced streaks. As you move, 

the light streaks move too. If 
you step outside or look through 
any of the car's other windows, 
however, you won't see them. 
What causes these streaks? Are 
they as prevalent when it's not 



Color of a city haze 

If you've lived in a large city, you 
almost certainly have spent part of 
your life in a haze. Why are such 
hazes brown? Is it due to some 
kind of selective absorption of the 
light? If so, by what? Or is it due 
to dispersive scattering of the 
light? Might it depend on what 
you're looking at through the haze? 

/ 1 12; 1 163; 1 164. 

"You win a little and you lose 
a little. Yesterday the air didn't 
look as good, but it smelled 
better. " 



If you stand on a mountain with 
your back to the sun and peer 
into a thick mist below you, 
there may be a series of colored 
rings around the shadow of your 
head. This set of colored rings, 
which may even be full circles, 
is called the glory (as well as 
the anticorona or brocken bow). 
You may momentarily feel 
divine when you notice that 
this beautiful and saintly 
display is around your head but 
not around a companion's. What 
causes this seemingly divine selec- 

Glories are now most often seen 
from airplanes. Next time you 
fly, sit on the side away from the 
sun, and watch for the glory around 
the plane's shadow on the clouds 
or mist below. I have seen three 
full spectrums at once, and as many 
as five have been observed and 

What causes the glory? Why does 
it surround the shadow of your 
head? What is the color sequence 
in each ring? How does the glory 
depend on the size of the particles 
in the mist? 

164, p. 555; 165, pp. 180-184; 
360 f pp. 68-70; 361 , pp. 4-5; 
362, pp. 138-139; 380; 536, 
p. 131; 954, pp. 224-225; 983, 
Chapter 7; 1016; 1017; 1019; 

1028, p. 130; 1 149 through 1 156; 

1499; 1626. 

134 The flying circus of physics 



Why are the sun and moon some- 
times surrounded by bright bands, 
called coronas? Usually there is 
a single white band, but occasional- 
ly there will be blue, green, and 
red bands outside the white one. 
If you're lucky, you may even see 
two such spectrums. What causes the 
brightening, and why can you dis- 
tinguish colors only occasionally? 
What determines the corona's width 
Can you predict the color arrange- 

164, pp. 547 ff; 165, pp. 178 ff; 
360, pp. 78-79; 536, pp. 130- 
131; 954, pp. 214-219; 983, 
Chapter 5. 


Frosty glass corona 

Walking past a frosty store window 
on a cold winter night, you may 
find the interior lights of the store 
surrounded by colored rings. At 
first thought, these colored rings 
seem to be the same as in the 
solar and lunar coronas. In 
the store window, though, the 
image of the light is surrounded 
by a black band, not a white 
band as in the coronas discussed 
above. Why is there a difference? 
And again, what is responsible for 
the colored rings? 

954, pp. 219-221; 983, p. 
157 ff. 


Bishop's Ring 

A different type of corona (and 
a much larger one, being about 
15° in angular radius) is the white 
and red-brown Bishop's Ring caused 
by volcanic dust spewed into the 
atmosphere. (After some volcanic 
eruptions the twilight sun turns a 
beautiful gold, the twilight sky 
colors take on a brilliant richness, 
and one can also see a second 
purple light* which lasts for hours 
after sunset.) What size particles 
are responsible for the red-brown 
color if that color is present? Will 
the Bishop's Ring be colored if 
there is a large range of particle 

164, p. 555; 165, pp. 178, 
191; 536, p. 130; 954, p. 282; 
983, pp. 167, 243; 1 104 through 
1 108; 1 109, pp. 430-434, 44 1; 
*See Prob. 5.60. 


Streetlight corona 

On your nighttime walk you may 
also be struck by the colored rings 
around the streetlights you pass. 
Is the same physics responsible for 
this corona as for the solar and 
lunar coronas and the store-light 
coronas? There is a simple test to 
show that there is at least some 
difference. If you screen off the 

streetlight, a store's interior lights, 
and the moon or sun, do the 
coronas in all three cases re- 
main? If any one disappears, then 
you should explain why it is dif- 
ferent from the others. 

954, pp. 221-223; 1091, pp. 
224-225; 1 157; 1 158. 


Blue moons 

My grandmother is from Aledo, 
Texas, where the population is 
about 100 people, dogs, and 
chickens. According to her, ex- 
citement comes to Aledo only 
once in a blue moon. But how 
often does a blue moon come? 
In fact, why would the moon 
ever be blue? Can there be blue 
suns too? Is either the moon 
or sun ever green? 

536, p. 12 1; 954, pp. 298-299; 
983, p. 242; 991; 1014, p. 421- 
423; 1 101; 1 159 through 1 162. 


Yellow fog lights 

Why are car fog lights yellow? 
Does it really help to have them 
yellow? Does it matter whether 
you're driving in the city or in 
the countryside? 

983, p. 244; 1111, p. 40. 

She comes in colors everywhere 1 35 


Blue hazes 

There is a colorful but mysterious 
haze that appears over vegetated 
areas relatively free from man- 
made contamination. The Blue 
Ridge Mountains of Tennessee and 
the Blue Mountains of Australia 
are both well known for their 
beautiful blue haze. What causes 
this type of haze? Smoke? No, 
because the haze is found in 
relatively uninhabited areas. 
Windswept dust? No, because the 
haze has the deepest blue during 
very light winds. Finally, the 
haze cannot be fog, because the 
blue is most common during warm 
summers. What, then, causes the 
haze, and why is it blue? 

/ 7 12; 1 165; 1 166. 


Shadows in muddy water 

Why can you see your shadow 
in slightly muddy water but not in 
clear water? Why can you see 
shadows of other people only if 
the water is very muddy? 

You might also notice the 
colors ground shadows in slightly 
muddy water. The edges closest to 
you are colored differently from 
those farthest from you. What 
causes this coloring? Does the color 
of the edges depend on whether 
you are facing toward or away from 
the sun? 

954, pp. 332-333; 1565. 


Color of milk in water 

After adding a few drops of milk 
to a glass of water, look through 
the glass at a white light such as a 
light bulb. The source will appear 
to be red or pale orange. Next look 
at the light reflected from the glass. 
The light will be blue. Why is 
there such a remarkable change of 

360, pp. 60-61. 


Color of cigarette smoke 

If you closely examine the smoke 
rising directly from a cigarette, 
you'll find that the smoke is 
slightly blue. If the smoke is in- 
haled and then blown out, how- 
ever, the smoke is white. Why is 
there a change? (It is not due to 
removal of tar and nicotine.) 

155, p. 4 1 1; 360, p. 62; 533, 
p. 147; 536, p. 383; 954, p. 
236-237; 983, p. 235. 


Color of campfire smoke 

A similar change of color is ap- 
parent in campfire smoke. When 
it is viewed against a dark back- 
ground (trees, for example), the 
smoke appears to be blue. Higher 

up, however, when it is seen 
against a light sky, the same smoke 
appears to be yellow. Why does it 
change its color? 

533, p. 147; 954, pp. 235-237, 


Oil slick and soap film colors 

Why do oil slicks on the street 
display colors? How thick are these 
slicks? Must the street be wet? 
Can you see them on overcast 
days or only in direct sunlight? If 
you can calculate the width of one 
of the colored rings, compare your 
number with a measured width. 
Will the finite size of the sun 
change the theoretical width of the 
rings in any way? 

Why do you see colors in soap 
films? How thin are the soap films, 
and in what thickness range will 
they show colors? Why that range? 
Why are some parts of some films 
black? Finally, why is there such 
a sharp boundary between the 
colored and black areas? Shouldn't 
there be a gradual change? 

322; 528 through 531; 533, 
pp. 139 ff. 


Color effects after swimming 

Why do you see colored rings 
around lights after you've been 

136 The flying circus of physics 



crystal structure 


Liquid crystals 

If a deformable container con- 
taining a liquid crystal is 
squeezed, colors appear around 
the squeezed area. The particular 
colors you see, however, will de- 
pend on your angle of view. How 
do the angle dependence and color 
sequence compare with those of 
an oil slick? If there is a difference, 
can you explain it? 

1081; 1132 through 1137. 


Butterfly colors 

Why are the wings of butterflies 
colored? Are the colors due to 
pigmentation? In some wings, 
yes, but in others, such as for 
the Morpho butterfly, the colors 
do not arise from any pigmenta- 
tion. A possible clue to their 
origin may be found by look- 
ing at a wing from several differ- 
ent angles: the wing takes on 
slightly different colors for dif- 
ferent viewing angles. Why? 

/ 138 through 1 142; 1625. 



Dark lines in a fork 

You have probably seen the dark 
line which lies between your 
finger and thumb when they're 
almost touching (Figure 5.95). 
You can see many such dark lines 
by looking through a fork's 
prongs as you rotate the fork. 
What's responsible for these dark 
lines? Can you predict whether 
the spacing between the lines will 
decrease or increase for a given 
turn of the fork? 

170, p. 487. 


Figure 5.95 

Dark line seen between two 



Eye floaters 

What are the tiny, diffuse spots 
you often find floating in your 
field of view? Are they illusions? 
Are they bits of dust on the eye's 
surface? Or are they objects with- 
in the eye? By looking at a bright 

light source through a pinhole in 
some opaque material, you'll find 
a beautiful array of floating con- 
centric circles and long chains 
(Figure 5.96). If the spots are 
merely shadows, then why do 
you see concentric circles and 
chains? Also, why does a pinhole 
help you see the structure of the 

170 f p. 530; 1091, Vol. 1 , pp. 
204 ff; 1167; 1168; 






Figure 5.96 

Structure of the floaters in your 



Points on a star 

What causes the occasional spiked 
appearance of car headlights? The 
cause cannot be entirely physiologi- 
cal since photographs of the head- 
lights also show spikes. Similarly, 
what causes the spikes found in 
star photographs? Is it possible to 
find any number of spikes on a 
star or a headlight photograph? 
In particular, can you find a star 
with an odd number of points? 

1169, p. 3. 

She comes in colors everywhere 137 


Figure 5.98 

Demonstration to show Poisson spot 


Poisson spot 

Why is there a bright central spot 
in the shadow of a small disc or 
sphere (say, two millimeters in 
diameter), whereas larger objects 
give ordinary dark shadows? By 
using a cardboard tube and a 
screen as shown in Figure 5.98, 
you'll find that not only is there 
a bright central spot in the shadow 
of the disc or sphere, but the 
shadow is actually composed of 
multiple dark and bright rings. 
What causes the central spot, which 
is called the Poisson spot,* and 
the rings? Why aren't they found 
in your own shadow? 



Pattern on screen 

in the shadow of a small sphere. 

204; 1 169, p. 200; 1 170, pp. 

*When Fresnel defended his dissertation 
before his committee in the 1800s, one 
of the committee members, Poisson, 
remarked that if the dissertation were 
correct, there would be a bright spot in 
a spherical object's shadow. This result 
clearly being ridiculous, he concluded 
that the dissertation must be wrong. 
But as a matter of fact, the spot had 
been seen some 50 years earlier and, 
soon after Poisson's conclusion, Arago 
rediscovered the central bright spot. 
In spite of all this, in one of those 
curious twists in the history of physics, 
it is the objector's name that is as- 
sociated with the spot. 





Eclipse shadow bands 

For several minutes before and 
several minutes after a total solar 
eclipse, dark bands called shadow 
bands race across the ground. The 

bands are separated by several 
centimeters and are about two 
centimeters wide. What could 
cause these bands? And why do 
they appear during an eclipse? Are 
they produced in our atmosphere, 
or are they made when the sunlight 
passes the moon? 

1171 through 1181; 1561. 


Sunset shadow bands 

Another set of shadow bands has 
been seen during normal sunsets. 
Ronald Ives (1182) has reported 
six observations in 15 years, all 
of which were from high points 
looking down on flatlands. These 
bands were several miles wide and 
moving at about 40 miles per 
hour. Are these bands another 
example of shadow bands? In any 
case, what causes them? 



Bands around a lake's reflection 

As you fly toward a distant small 
lake, eventually reaching the 
angle for optimum reflection of 
the sun, why are there alternating 
dark and bright bands around the 
principal reflection from the lake? 

360, p. 12. 



turbulent cells 


Star twinkle 

My mother taught me to say, 
"Twinkle, twinkle, little star. . ." 
Why does a star twinkle? Ap- 
proximately where is the 
twinkling produced? Does a star 

1 38 The flying circus of physics 

change colors or move around 
because of the twinkling? Does it 
twinkle more in the winter or 
summer? Does a red star twinkle 
more than a white star? Do you 
see twinkling when you use a 
telescope? Do the moon and 
planets twinkle? 

What causes the shimmer of an 
object when you view it over 
heated surfaces such as, for 
example, hot car tops or roadways? 
How high above the heated surface 
will your viewing be affected? Is 
it the air closest to you or farthest 
from you that dominates the 

164, pp. 462-466; 165, pp. 166- 
169; 954, pp. 63-71; 983, pp. 
17-19; 11 11, pp. 80-81; 1183 
through 1188. 



Bleaching by light 

How does sunlight fade colored 
clothing? Does the rate of fading 
depend on the color? Why does 
sunlight or fluorescent light cause 
oil paintings to fade? Why are 
some foods and beverages, such as 
beer, shielded from sunlight? Is 
any particular light frequency most 

466, pp. 214-215. 

radiation forces 



Optical levitation 

Earlier in this book we discussed 
levitation of balls by air currents 
and water jets* and in both cases 
there was surprising stability. 
Light can also levitate and stabilize 
balls, for light from a relatively 
powerful laser has lifted and held 
in suspension transparent glass 
spheres of about 20 microns in 
diameter (Figure 5.104). How 
can light lift such a sphere against 
gravity? And how is stability 
against sideward motion provided? 

1189 through 1191. 

*Probs. 4.20 and 4.22, 

Figure 5.104 

Glass sphere suspended in an 
upward directed, expanding 
laser beam. [After A. Ashkin 
and J. M. Dziedzic, Appl. Phys. 
Let, 19 (8), 283 (1971).] 



Lights through a screen 

Car headlights viewed through a 
screen look very different than 
when they are viewed without 

a screen (Figure 5.105). What, 
in detail, causes the difference? 
533, p. 163. 




No screen With screen 

Figure 5.105 

The change in the appearance of a light when viewed through 
a window screen. 

She comes in colors everywhere 1 39 

blackbody emission 

atmospheric transmission 


Star color 

Some stars look red. Some look 
white. Are there blue stars? Or 
green stars? 


Luminous tornado 

There have been many reports, 
including published accounts, 
describing mysterious lights as- 
sociated with tornadoes. Though 
they are generally dismissed as 
illusions, there has been at least 
one published photograph (1192, 
1193) that apparently shows 
luminous columns in two 
nocturnal tornadoes. Eyewitness 
accounts of these particular 
tornadoes gave exciting descrip- 
tions of the light emission. 
The beautiful electric blue 
light that was around the 
tornado was something to 
see, and balls of orange and 
lightning came from the cone 
point of the tornado (1193).* 
In another tornado occurence an ob 
server saw the following: 
I was looking. . . up at the 
clouds when I saw some- 
thing that looked like a 
searchlight beam extend 
out of the cloud and reach 

*Copyright © 1966 by the American 
Association for the Advancement of 

to the skyline. It seemed 

a bit brighter than the cloud 

background. Edges were 

very sharp, overall intensity 

even, sides parallel. Width 

about a degree of arc. No 

movement or turbulence 

evident. The phenomenon 

was interesting enough so 

I took out my Polaroid 

glasses and observed this 

"ray" through them, 

twisting the lens to look 

for polarization. No 

polarization was noted. 

This ray was obvious enough 

so that passersby on the 

street were staring at it. 

All this took, say, 60 to 

120 seconds (or more). 

Then abruptly the ray was 

instantly replaced by a 

normal tornado funnel. 

No transition stage was 

noted. The funnel did 

not descend from the 

cloud layer. It appeared 

over all, in situ (1193).* 
Although these phenomena are 
poorly understood, can you suggest 
causes for them, perhaps making 
some rough numbers to support 
your suggestions?* 

224; 225; 1 192; 1 193. 

*See Prob. 6.35 also. 



Sugar glow 

Late one night I was stirring some 
dry granulated sugar in a glass, 
which is kind of a late-at-night 
type of thing to do. Suddenly the 
lights went out. As I continued 
to stir, I saw brief flashes of 
light through the side of the glass. 
How did the mechanical stress 
and strain of my stirring cause the 
light emission? 

1194, pp. 121,292,378-387; 


Suntans cind sunburns 

What actually causes suntans and 
sunburns? Is the same wave- 
length range of light responsible 
for both? Why is it more difficult 
to get sunburned once you have a 
tan? Can naturally dark skin be- 
come sunburned as easily as 
lighter skin? What do suntain oils, 
lotions, and creams do to prevent 
sunburn and promote suntan? The 
pertinent point is, of course, 
whether they really do what the 
advertising claims. If they inhibit 
whatever causes sunburn, won't 
they inhibit suntan also? 

Why are burning and tanning 
less likely when the sun is low or 
when you're behind glass? Why 
are they more likely at the beach 
than in a grassy backyard? 

344, pp. 19-22; 466, p. 212; 
1203; 1512. 

140 The flying circus of physics 




Catching fireflies at my grand- 
mother's house was one of the 
most enjoyable times of my 
childhood (Figure 5.110). I have 
read that the synchronous flashing 
of Asiatic fireflies is even more 
Imagine a tree thirty-five 
to forty feet high thickly 
covered with small ovate 
leaves, apparently with a 
firefly on every leaf and 
all the fireflies flashing 
in perfect unison at the 
rate of about three times 
in two seconds, the tree 
being in complete dark- 
ness between the 
flashes. . . . Imagine a 
tenth of a mile of river 
front with an unbroken 
line of. . .trees with fire- 
flies on every leaf flash- 
ing in unison, the in- 
sects on the trees at the 
ends of trje line acting 
in perfect unison with 
those between. Then, 
if one's imagination is 
sufficiently vivid, he 
may form some con- 
ception of this amazing 
spectacle (1196). 
What mechanism produces the 
light we see? That light is often 
referred to as cold light, implying 
there is no energy lost to heating. 

(An incandescent bulb, on the 
other hand, is a hot light.) Is the 
firefly 100 percent efficient in 
converting energy to the form of 
light? What color is the light? Why 
that color? Finally, how do the 
Asiatic fireflies lock themselves 
into a chorus of synchronous 

1090, Chapter 4; 1 194, pp. 538- 
554; 1196 through 1201; 1458; 
1585; 1624. 



Other luminescent organisms 

Many other organisms produce 
their own light, too. The 
Brazilian railroad worm, for 
example, has a red light on its 
head and green lights down its side. 
Another type of luminescent 
organism, the dinoflagellates, will 

set the sea on fire" when disturbed 
during the day (by a boat, say) 
but during the night they will 
respond with a blue glow. One type 
of crustacean, when dried, can be 
made to glow by moistening. Such 
a light source was used by World 
War II Japanese soldiers when a 
stronger light was too dangerous. 
Spitting on a bit of dried crustacean 
would give off enough light to 
read a map. 

There have been many other, 
but less common, examples of 

By permission of John Hart. 
Field Enterprises. 

She conies in colors everywhere 141 

natural luminescence. In one 
case, cut potatoes glowed suf- 
ficiently that one could read by 
them in an otherwise dark room. 
There has even been a case in 
which a corpse glowed in the 
dark. But the most disturbing, 
especially if one is relying on 
darkness to conceal a slight 
indiscretion, have been the times 
in which urine glowed in the 

In the case of the dinoflagellates, 
why do they glow red during the 
day but blue during the night? 
In all these various examples, what 
causes the luminescence? 

1 194, pp. 457-492; 1200 
through 1202; 1458. 




Photosensitive sunglasses 

Some sunglasses are clear indoors 
but darken immediately upon 
exposure to sunlight. The change 
is reversed soon after the sunlight 
is eliminated. What causes this 
reversible change in the transmis- 
sion properties of the glass? 

984; 1204. 



Black- light posters 

How does a black-light poster 
work? Why does the same physics 

allow some soap manufacturers to 
claim that their products get clothes 
"whiter than white"? 

1205, p. 70. 




Fluorescent light conversion 

How is ultraviolet light created and 
then converted to visible light in 
a fluorescent lamp? How fast 
should the conversion be? You 
don't want it so fast that the lamp's 
output shows the 60 cycles per 
second of the line voltage used to 
excite the tube. But then again, 
you don't want the lights to stay 
on long after you've turned off 
the switch. 

466, pp. 233-240; 1205, p. 76. 


(5.115 through 5.141) 




Speckle patterns 

If you look at a smooth, flat-black 
piece of paper at a 45° angle in 
direct sunlight, you will see a grainy 
speckle pattern of various colors 
dancing on the paper. Similar pat- 
terns are more commonly made 
with laser light, but sunlight is cer- 

tainly more convenient. In either 
case, the pattern will move if you 
move your head, but whether it 
moves in the same or opposite 
direction as your head will de- 
pend on whether you have normal, 
nearsighted, or farsighted vision. 
What causes these speckle patterns, 
and why are there colors in the 
sunlit patterns? Finally, can you 
explain the movement of the pat- 
tern and its dependence on your 

1206 through 1209; 1560. 

stroboscopic effect 


Humming and vision 

If you hum while watching tele- 
vision from a distance, horizontal 
lines will appear on the screen, and 
you can make them migrate up or 
down or remain stationary by 
humming at the appropriate pitch. 
In a similar demonstration, a black- 
and-white-sectored disc is rotated 
on a turntable. If you use a strobo- 
scope to illuminate the disc, you 
can freeze the rotating sectors or 
make them slowly migrate one 
direction or the other by choosing 
a suitable flashing frequency. How- 
ever, you can also do this by merely 
humming at the proper pitch. Why 
does humming effect your vision 
in this way? 

1210; 1211. 

142 The flying circus of physics 

visual latency 

stroboscopic effect 

light intensity 

No filter: regular swinging 

Filter over one eye 

Filter over other eye 

Figure 5.117 

A normal pendulum swing changes to a circular motion 

if a polarioid filter is placed over one eye. 


Sunglasses and motion distortion 

With a dark filter over one eye 
(say, half a pair of sunglasses), 
watch the swing of a simple 
pendulum. Even though you know 
the pendulum's motion is in one 
plane, the pendulum appears to 
revolve in an ellipse when the filter 
is in place (Figure 5.117). To 
the uninitiated, the surprising re- 
sult can be quite striking. . . and 
mysterious. The apparent three- 
dimensional motion can be en- 
hanced by hanging a string from 
the pendulum's pivot, for then 
the string acts as a reference ob- 
ject and the pendulum appears 
to turn about it. 

If you should drive while wearing 
only half a pair of sunglasses, a 
car passing on your left will seem 

to have a considerably different 
speed than one passing on your 
right even if they actually have the 
same speed. In neither case is the 
apparent speed the correct one. 
In addition, the apparent distances 
of objects in the landscape will be 
wrong and even dependent on 
which side of the car the objects 

What causes the apparent three 
dimensional motion of the pendu- 
lum? What exactly does the filter 
have to do with this motion and 
the distortion of a car's speed 
and the distance of objects in the 

1212 through 1222; 1541 
through 1543. 


Top patterns before TV screen 

If a flat top with a surface design 
is spun before a TV screen (with 
a stable picture and in an other- 
wise dark room), psychedelic pat- 
terns appear on the top's surface. 
Undoubtedly the pattern stems 
from the top's surface design, 
but why is the light of a TV needed? 

170, p. 36. 


A stargazer's eye jump 

Why do you have a better chance 
of seeing a dim star neighboring 
a bright star if you jump your 
eyes to one side of the stars? 

332 f Vol. 1,p. 35-3; 41 2 f p. 


Retinal blue arcs 

Blue arcs of the retina are 
another physiological problem cur- 
rently receiving attention. Purkinje 
first reported seeing them from 
glowing tinder as he was kindling 
a fire. For about 30 seconds he 
saw two blue arcs extending from 
the tinder. You can see them your- 
self* under controlled circumstances 

She comes in colors everywhere 143 



Figure 5.120 

Blue arc in your left eye's 
field of view. [After J. D. 
More land, Vision Research, 8, 
99 (1968).] 

by using small holes punched into 
a card that is then placed over a 
light. After sitting in the dark 
about a minute (don't wait too 
long), switch on the light. Depend- 
ing on the hole's shape, various 
shaped blue arcs (e.g., Figure 
5.120) can be seen for up to a 

What causes these arcs— scattered 
light inside the eye? Why, then, 
are they always blue? Shouldn't 
they depend on the color of the 
scattered light? Perhaps they are 
due to bioluminescence. Or may- 
be they could be due to a secon- 
dary electrical stimulation of nerve 
fibers or neurons by other active 
nerve fibers. If the latter is true, 
the shape of the arcs as a function 
of stimulus shape should tell us 
something about the retinal 
topography. In any case, we still 
have to explain why the arcs are 

1224 through 1227. 

*One of Moreland's several papers (1224) 
describes in further detail how to opti- 
mize the observation and how to de- 
monstrate it to a small audience. 



Prisoners confined to dark cells 
see brilliant light displays (the 
"prisoner's cinema") in their 
perfect darkness. Truck drivers also 
see such displays after staring at 
snow-covered roads for long 
periods. In fact, whenever there 
is a lack of external stimuli, these 
displays- called "phosphenes" - 

appear. They can be made at will, 
however, by simply pressing your 
fingertips against closed eyelids, 
and some hallucinogenic drugs 
apparently give magnificent 
phosphene shows. They can also 
be produced by an electrical shock. 
In fact, it was high fashion in the 
eighteenth century to have a 
phosphene party (even Benjamin 
Franklin once took part) in which 

visual latency 

light intensity 


Streetlamp sequence 

Sometime when you're driving at 
dusk, watch the streetlights turn 
on: they brighten in sequence 
down the street. Does it really 
take electricity that much time 
to travel from lamppost to lamp- 

post? If there are intersections 
with several streetlamps, you'll 
find those lamps turning on 
sooner than the lamps between 
intersections (Figure 5.122). 
This certainly can't be due to 
a lag of electricity. Why, then, 
are there time lags between the 

1212 through 1222. 

Figure 5.122 

1 44 The flying circus of physics 

a circle of people holding hands 
would he shocked by a high-volt- 
age electrostatic generator, phos- 
phenes being created each time 
the circuit was completed or 

In 1819 the Bohemian 

physiologist Johannes 

Purkinje published the 

most detailed account 

of phosphenes. He 

applied one electrode 

to his forehead and the 

other to his mouth, and 

by rapidly making and 

breaking the current 

with a string of metal 

beads, he was able to 

induce stabilized phos- 

phene images (1223). * 

Phosphene research is no longer 
so academic, because recent work 
has shown that those blind people 
who experience phosphene dis- 
plays may someday be given 
artificial vision by use of those 
diplays. A miniature TV camera, 
placed inside an artificial eye, 
would send its electrical signals 
to a small computer located inside 
a pair of eyeglasses. The computer 
would in turn stimulate the brain 
by a network of electrodes that 
had been placed adjacent an 
occipital lobe. When the TV 
camera detected an object in its 
left field of view, for example, 
the computer would stimulate 
the electrode that would produce 
a phosphene image in the left 
portion of the person's field of 
view. The person would therefore 
see the external world. 

Why are such visual displays 

produced under electrical and pres- 
sure stimulations or when there is 
an absence of external stimuli? 

1223; 1572; 1573. 

*From "Phosphenes" by Gerald Oster. 
Published in Scientific American. Copy- 
right © 1970 by Scientific American, 
Inc. All rights reserved. 


Spots before your eyes 

If you stare at a clear sky you will 
find your entire field of view 
covered with moving specks. Those 
specks are always present, but 
usually you don't notice them. 
(Why is that?) 

Although the jerking motion ap- 
pears to be random, if you feel your 
pulse while watching the specks, 
you will find the motion correlated 
with your pulse and also see that 
the specks always follow certain 
routes in your field of view. What 
are the specks, and what causes the 
jerking along those particular 

1091, Vol. 1,pp. 222-223; 1168; 
1233, pp. 407-408. 


Purkinje's shadow figures 

Close your eyes, place a hand over 
one, turn to face a bright light, and 
wave your other hand back and 
forth across your face so that the 
shadows of your fingers repeatedly 
cross over your closed, but ex- 
posed, eyelid. In the center of 

your field of vision you'll see a 
checkerboard array of dark and 
bright squares, and down from 
the center there will be either 
hexagons or just irregular figures. 
If you're using the sun as the 
light source, you'll also see eight- 
pointed stars and various spiral 
lines. What causes these several 

1091, Vol. 2, pp. 256-257; 1234. 


Early morning shadows in your 

If you stare at a sunlit room im- 
mediately upon opening your eyes 
after a night's sleep, why will you 
briefly see dark images in your 
field of view? If the images are 
shadows of objects in your eye, 
then why don't you see the 
shadows all the time, and why 
do they fade so quickly after 
this early morning glimpse? 

1091, Vol. 1,pp. 212 ff; 1168; 
1233, pp. 406-407; 1235 

color perception 


Purkinje color effect 

In dim light a particular blue may 
be brighter than a particular red, 
but in good illumination the rela- 
tive brightness may be reversed. 
Why should the relative brightness 
of reds and blues depend on the 
illumination level? 

332, Vol. 1, p. 35-2. 

She comes in colors everywhere 145 


Mach bands 

How sharp is your shadow's edge 
when you stand in a strong light 
such as sunlight? If you look care- 
fully, you will see two shadows, the 
darker one neatly inside the other. 
The inside contour of the lighter 
shadow has a dark band; the out- 
side contour has a bright band. 
There is nothing unique about 
your body, because every shadow 
has such edge patterns (though 
more than one light source will 

complicate the patterns, of course). 
Figure 5.127 shows how the edge 
pattern can be seen with a piece 
of cardboard held in front of a 
fluorescent lamp. Why are the 
bright and dark bands and your 
half-shadow present? Can they 
be photographed?* 

954, pp. 129-132; 1228, 
Chapter 2; 1229 through 1232. 

*ln early attempts to measure the X-ray 
wavelength, some physicists used what 

they thought were X-ray diffraction pat- 
terns resulting from the passage of X 
rays through common diffraction slits. 
They did find light and dark patterns on 
their films, and using those patterns they 
calculated the wavelength. Unfortu- 
nately, later work revealed that these pat' 
terns you see in your own shadow and 
were not at all indicative of X-ray dif- 
fraction (1228). 

Figure 5.127 

Mach bands can be seen in the card's shadow with this arrangement. If the lamp is one foot above a white 
sheet of paper, then place the card one or two inches above the paper. Small horizontal motions of the 
card may help you see the bands better. The graph shows the luminosity for various points on the paper. 
(Figures from Mach Bands: Quantitative Studies on Neural Networks in the Retina by Floyd Ratliff 
published by Holden-Day, Inc.) 

146 The flying circus of physics 

Land color effect 

color perception 


Seeing the colors of your mind 

If an object looks blue, blue light 
must come from the object, right? 
In fact, each color you see corre- 
sponds to light with a certain fre- 
quency or a combination of several 
frequencies. This seems very 
reasonable, but Edwin Land threw 
a wrench into the explanation with 
a few simple experiments that you 
can do yourself. 

What do you have after making 
two black-and-white slides of a 
colored scene, using a red filter 
for one slide and a green filter 
for the other? Why, two black- 
and-white pictures of course. 
How can you get anything else 
with black-and-white film? 

But now, using two projectors, 
simultaneously project those 
slides onto a screen (Figure 5.128). 
Use a red filter with the slide made 


M Re< 

Projector with 

slide made in 

red light 

Red filter 

Projector with 

slide made in 

green light 

Figure 5.128 

Projection arrangement to 

show Land color effect. 

with the red filter; the normal white 
projector light is sufficient for 
projecting the "green" slide. What 
do you see on the screen? Although 
each slide is only black and white, 
and the only colored light you 
use is red, the superimposed pro- 
jection gives the full range of color 
in the original scene. 

There is nothing special about the 
filters used. All you need are two 
different colors or even one color 
and one white light. Both slides 
can even be made in a single color 
as long as the light frequency used 
for one slide is at least slightly 
different from the light frequency 
used for the other. 

What causes this recreation of 
the color of the original scene even 
though the color information is 
seemingly lost in the individual 
slides? Once again, if an object 
looks blue, must blue light neces- 
sarily be coming from that object? 

1236 through 1239; 1566; 1567. 

chromatic aberration 


Making colors with a finger 

Watching with only one eye, move 
a finger across your view of a sun- 
lit window that is across the room 
from you. When the finger first 
begins to block and distort the 
image of the window, the side of 
the image nearest the finger turns 
yellow-red (Figure 5.129). As 
your finger reaches the opposite 
side of the image, that opposite 
side turns blue. (You can see the 
same thing using an incandescent 
bulb, but the blue is fainter.) Why 






Figure 5.129 

[After S. F. Jacobs and A. B. 

Stewart, Amer, J. Phys., 20, 247 


do the colors appear, and why 
are the opposite sides of the 
window's image colored differently? 

533, pp. 104-105; 1091, Vol. 1, 
pp. 175-176; 1516. 

color perception 


Colors in a black and white disc 

Is it possible to see colors in black 
and white surfaces? Normally, it 
isn't, but try the following: con- 
struct a disc of alternating black 
and white sectors, and then as the 
disc is spun at low speed, concen- 
trate on it (but ignore the individ- 
ual sectors). After a few minutes 
you'll find that the leading edges 
of the white sectors will turn red, 
the trailing edges blue. (Different 
shades will be seen for different 
illumination levels.) At a faster 
speed the whole white sector will 
be pink-red, and a green-blue 
will cover part of the black section. 
With a still-faster speed, the colors 
cannot be distinguished but little 
sparks of violet-pink and green- 

She comes in colors everywhere 147 

Figure 5.130 

Disc that shows colors when spun. 
gray light seem to jump about. 
The disc in Figure 5.130 will give 
all three effects simultaneously. 
Why do you see those colors? 
Why must you watch the disc for 
several minutes before the colors 

332, Vol. 1,p. 36-1; 1091, Vol. 
2, pp. 255 ff; 1231; 1240; 1241. 





Color effect from fluorescent 

If the disc described above is 
rotated faster (about 5 to 15 rps), 
the color effects disappear. But 
if it is put under a fluorescent 
light, a new color effect will appear: 
you will see two concentric rings 
that are composed of alternating 
red, blue, and yellow bands. You 
can also see colored fringes -yellow 
or orange, depending on the back- 
ground -if you watch a spinning 
coin under a fluorescent lamp. 
Why does the fluorescent lighting 
cause these color effects? Can they 
be photographed? 

1242 through 1246. 


Floating TV pictures 

While watching TV in an other- 
wise dark room, quickly run your 
eyes from about a foot to the 
left of the screen to about a foot to 
the right. You will see a bright, 
detailed, ghostlike image of the TV 
picture floating in space to the 
right of the screen (Figure 5.132). 
You may even see three or four 

images, all right-tilted parallelo- 
grams. Why are these ghost images 
formed, and what's responsible 
for the tilt? Do you see the same 
sense of tilt if you move your 
eyes in the opposite direction ? Are 
there ghost images for a rapid ver- 
tical scan of your eyes? 


Figure 5.132 

Ghost images of TV picture. 


3-D movies, cards, and posters 

There are two methods of making 
commercial three-dimensional 
movies and comic books. One 
method involves printing pictures 
in two colors, red and green, and 
then using cheap glasses with red 
cellophane over one eye and green 
over the other. The other method 
employs polarizers in the glasses 
and in front of the two projection 
cameras, and the cameras project 
simultaneously onto the screen. 
How do these methods give a 
stereoscopic illusion? As you 
probably know, three-dimensional 
movies have not gained widespread 
popularity, which means that there 
must be some drawbacks. Other 

than the annoyance of wearing the 
glasses, what are the problems? 

How is the 3-D effect gained in 
3-D baseball cards and postcards? 
Some bright red and blue posters, 
paperbacks, etc. give an impres- 
sion of depth if red letters are 
printed on a blue background: the 
letters appear to be closer to the 
viewer than the background. Why? 
Do such depth illusions with dif- 
ferent colors depend on the illu- 
mination level? What other methods 
can produce a stereoscopic illusion? 

533, pp. 105-106; 1070, pp. 107- 
1 10; 1092; 1213; 1255 through 
1260; 1591 through 1607. 

148 The flying circus of physics 


Enlarging the moon 

Probably the most striking illusion 
in the natural landscape is the 
apparent enlargement of the moon 
when it is near the horizon (Figure 
5.134). Is this illusion brought 
about by atmospheric conditions, 
or is it a psychological effect? Can 
you estimate the apparent enlarge- 

165, pp. 154- 155; 533, pp. 62- 
63; 954, pp. 155-166; 1248 
through 1253. 

Figure 5.135 


Rays of Buddha 

Occasionally you will see a sunset 
in which brilliant rays of light 
emerge from the setting sun, fan- 
ning out across the western sky (Fig- 
ure 5.135). This display is caused by 
mountains or clouds blocking part 
of the sunlight. What color are 
the rays? What color is the sky 
against which you see the rays? 
Not as frequently you will see 
rays of light converging to the 
antisolar point in the east. Very 
rarely you may see those rays 

emerging from the solar point in 
the west, arcing across the entire 
sky and converging to the antisolar 
point in the east. But wait. How 
could a cloud or mountain block 
part of the sunlight to give a fan 
display? After all, the sun is very 
far away from us, and the sun's 
rays should all be parallel. 

164, pp. 452, 567; 165, p. 185; 
954, pp. 275-277; 1513. 

By permission of John Hart. 
Field Enterprises. 


Moon-to-sun line 

Sometime when you find a crescent 
moon in the daytime sky, mentally 
draw a line along its symmetry 
axis (Figure 5.136). Does the line 
point to the sun? Shouldn't it? 

165, pp. 149 ff; 954, pp. 151- 
166; 1250 through 1254. 

Figure 5.136 

Shouldn't the line through the 

crescent moon point to the 'sun? 



She conies in colors everywhere 149 


Bent search beams 

When seen from the side, search- 
light beams appear to bend over. 
Does the beam really get scattered 
or refracted downward by the 

165, pp. 149 ff; 954, pp. 151- 
166; 1250 through 1254. 


Rear lights and a red light 

If, while driving at night, you 
should be about a block behind 
a car approaching a red light, the 
rear lights of that car may appear 
to stop somewhere beyond the 
intersection. When you reach the 
red light yourself, however, you 
find the other car waiting as it 
should be in front of the red 
light. What causes this particular 


light flux 




What causes snowblindness (white- 
out)? After long exposure to the 
white light of snow and ice fields 
your eyes feel as though they were 
full of sand. Intense pain may fol- 
low for days. Is snowblindness 
more likely to occur on a sunny 

or a cloudy day? In his diary and 
stories of five years of polar ex- 
peditions, Vilhjalmur Stefansson 
. . .it might be inferred that 
snowblindness is most likely 
to occur on days of clear 
sky and bright sun. This 
is not the case. The days 
most dangerous are those 
when the clouds are thick 
enough to hide the sun 
but not heavy enough to 
produce what we call 
heavily overcast or gloomy 
weather. . .everything looks 
level. . .You may collide 
against a snow-covered ice 
cake as high as your waist- 
line and, far more easily, 
you may trip over snow- 
drifts a foot or so in height 
.. .(1113).* 
In such conditions you can't even 
distinguish the horizon. What 
role do the clouds play in 
increasing the probability of 

1 1 13, pp. 149, 199-202; 1 122; 

*Vilhjalmur Stefansson, The Friendly 
Arctic, copyright © 1921 by the 
Macmillan Company. Permission 
granted by Mcintosh and Otis, Inc. 


Resolution of earth objects by 

What are the smallest objects or- 
biting astronauts can distinguish 
on the earth's surface? In particu- 
lar, can they see large cities in the 
day or night or other large objects 
such as the pyramids? The early 
Mars fly-bys were disappointing 
to many people, especially non- 
scientists, because their pictures 
showed no signs of intelligent life. 
What signs of intelligence could you 
see on the earth if your photos had 
a resolution of, say, one kilometer, 
which is a typical value for weather 
satellite photos? If that resolution 
is not sufficient, how much is re- 
quired to see signs of life? 

360, pp. 182-184; 1263 
through 1265; 1498. 


ray optics 



A Christmas ball's reflection 

A shiny Christmas tree ball can give 
you a picture of nearly the entire 
room in its reflection. How will it 
reflect a point source of light in an 
otherwise dark room? Hold a ball 
about 10 centimeters from one eye 
and catch the reflection of the 
point source. (A pinhole punched 
in foil that covers a lamp provides 
a good point source.) The reflected 
image is an extended line of light, 

150 The flying circus of physics 

not a point. But, immediately after 
switching on the room lights, the 
line of light quickly contracts to 
an undistorted image of the point 
source. First, why is there a distor- 
tion of the point image in the dark 
room? Second, why does the 
distortion depend on the illumina- 
tion of the room? 



Moire patterns 

If two similar patterns with 
slightly different periodicities 
are superimposed, a larger pattern, 
called a Moire' pattern, appears. 
You can easily see this by folding 
over a sheer curtain or by looking 
through a comb held at arm's 
length in front of a mirror. In the 
comb example, the comb and its 
image merge to form a larger comb- 
tooth pattern. For a more quanti- 
tive observation, place one metal 
sheet covered with circular holes 
several inches behind another such 
sheet to get a resultant circular 
Moire pattern when the screens 
are viewed together from a distance. 
How does the observed Moire 
pattern change with your distance 
from the screens? How does it vary 
with changes in the separation dis- 
tance of the screens? Which way 
and how fast does the Moire pattern 
move as you walk parallel to the 
screens? Finally, does the motion 
of the pattern depend on your dis- 
tance from the screens? 

954, pp. 85-87; 1267 through 

She comes in colors everywhere 151 

The electrician's evil 
and the ring's magic 


(6.1 through 6.5) 

joule heating 





What exactly happens to you 
if you touch a live wire? What 
is it that can hurt or kill you? 
The voltage? The current? 
Both 7 Are you burned? Is 
your heart's rhythm disturbed? 
How does the danger depend on 
the frequency of the current? 
In particular, why is Europe's 
50 cycles per second supposed- 
ly safer than America's 60 
cycles per second? Is direct 
current more dangerous than 
alternating current, or does it 
just depend on circumstances? 

You may not be killed out- 
right, but if you continue to 
hold on to the electrical 
component, you may eventual- 
ly die: the longer you wait, 
the lower your body's resis- 
tance becomes, and thus, 
you get closer to a lethal 
dose of current. Why does 
your body's resistance change 
with time? 

1273; 1274. 

Exceptionally good references: Singer 
(1349), Uman (786), Schonland (301), 
Malan (300), and Corliss (1611). 


Frog legs 

In a classic experiment dealing 
with the nature of nerves and 
muscles, Galvani (1780s) em- 
ployed a deceptively simple ar- 
rangement. A frog leg was hung 
from a bronze support that was 
bolted into an iron railing (Figure 
6.2). The hanging leg could also 
touch part of the railing, but 
every time it did, it contracted 
and was thrown into spasms. 
When the spasms died out, the 
leg would droop and touch the 
railing, and the contraction and 
spasms would begin again. What 
caused this reaction? Can you 
produce some numbers to sup- 
port your answer? 



Figure 6.2 

Frog leg sent into spasms when it 

touches the iron railing. 


Getting stuck to electric wire 

I f you should grab a "live" wire 
that passes about 25 milliamps 
through your hand, you prob- 
ably won't be able to release 
the wire? Why not? [Do not 
grab such a wire on purpose, 
for it may lead to your death 
(seeProb. 6.1)]. 



Electric eel 

How can an electric eel shock you? 
A healthy eel can produce some- 
thing like one amp at 600 volts. 
What could possibly be the source 
of such enormous power? Does 
the eel continuously discharge in 
the sea water? Why doesn't it 
shock itself? 

The navigational ability of 
aquatic animals has long been un- 
explained. Recent work, however, 
suggests that some of the animals 
may be able to detect electric fields 
created by ocean currents moving 
through the earth's magnetic field. 
These fields would supposedly help 
the animals orient themselves. First 
of all, can you show how the elec- 
tric fields would be produced by the 
moving water? Next, can you ex- 
plain how an animal could possibly 
detect such a small field? 

1276 through 1282. 

The electricians evil and the ring's magic 153 

Figure 6.5 

"When I was a little girl we 
didn't have microwave ovens, 
and sometimes it took a whole 
hour to prepare a meal. " 


electric field 


Microwave cooking 

An ordinary gas oven will cook a 
roast from the outside inward, but 
a microwave oven will cook the in- 
terior first. Hence, your micro- 
wave-cooked roast may be wejl 
done inside and pink outside. 
Should you be caught in front of a 
large, active radar dish or hold your 
hand inside a microwave oven, you 
too may be well done inside and 
pink outside. Why do microwaves 
cook this way? As a matter of fact, 
how do microwaves cook meat at 


electric current 



Time to turn on light 

When you turn on a light switch, 
how long does it take for the light 
to come on? Must you wait for 
the electrons in the wires to reach 
the light bulb? Once the current 
is flowing, how soon does the bulb 
begin emitting visible light? 



(6.7 through 6.18) 

charge separation 

electric field 



Shocking walk on rug 

Being shocked after walking across 
a rug or sliding across a car seat is 
a common experience. Granted 
that you must be building up 
charge somehow, can you explain 
more about what's happening? 
For instance, why must you walk 
across the rug-why doesn't the 
charge build up if you merely 
stand still? Why does the effect 
depend on the season? 

This electrifying experience 
is normally part of a physics class 
at some point: glass rods are 
vigorously rubbed with cat's fur- 
or something like that. Why are 
they rubbed? Will they charge 
less rapidly if they are rubbed 

less vigorously? Does friction 
actually have anything to do with 
the charging? And why does the 
polarity of the rod depend on 
what's rubbed against it? Finally, 
why is the charge decreased if 
the rod is held in the smoke of a 

300, pp. 168-170; 537; 1288 
through 1297. 


Kelvin water dropper 

Another common physics demon- 
stration is the Kelvin water dropper 
(Figure 6.8). Briefly, water drips 
through two tin cans, the cans being 
wired together as shown. After a 
short time, one connected pair of 
cans becomes positive while the 
other pair becomes negative. Why? 
The apparatus is seemingly sym- 
metric. How, then, do the two 
pairs develop opposite charges? 
In particular, can you explain how 
the charging first begins? 

155, pp. 261-262. 


Figure 6.8 

Kelvin water dropper. 

154 The flying circus of physics 


Electrical field and water streams 

Water streams, while initially well 
defined, eventually break up into 
drops. You can stop that breakup 
very easily by holding a charged 
object near the stream. If the ob- 
ject is fairly strongly charged, the 
stream will also be attracted to it. 
Can you explain these results? Of 
course, you really should first ex- 
plain why the water stream normal- 
ly breaks up. 

322, pp. 86-87, 91-95; 1283 
through 1287. 


Snow charging wire fences 

Electrical shocks are often as- 
sociated with blowing sand and 
snow. For example, with snow 
blowing in the Colorado Rocky 
area, "wire fences on the plains 
near the mountains frequently 
accumulate charges strong enough 
to knock over men or cattle, and 
sometimes spit sparks to nearby 
grounded objects. Plains residents 
occasionally report sparks that 
jump as much as a yard from 
their fences" (354). (One jumping 
an inch will knock you down and 
leave you sick for several hours.) 
Why does the blowing snow charge 
the fences? 

354, pp. 704-705; 1298 
through 1301; 1527. 


Scotch tape glow 

If you unroll scotch tape in a dark 
room, you'll see a brief glow along 
the line where the tape is being 
ripped from the roll. What causes 
the light emission? Does it have 
any particular color? If so, why 
that color? 

1 194, p. 252; 1302. 

Falling sugar 

At first Later 

Figure 6.12 


Sifting sugar 

One day as I was sifting confec- 
tioner's sugar for a cake frosting, 
a curious thing happened to the 
sugar. When I started, the sugar 
would fall straight down, but 
gradually more and more of the 
sugar would be thrown to the 
side (Figure 6.12). Why was it 


Gas truck chains 

Why in the past were chains dragged 
beneath gasoline trucks? Should 
you drag a chain from your car? 

1303 through 1306. 


Charge in shower 

When you take a shower, the 
splashing water produces negative 
charges in the room's air and elec- 
tric fields of up to 800 volts per 
meter. Similar negative fields are 
found near natural waterfalls. In 
addition, when large crude-oil car- 
riers are cleaned with high-velocity 
water jets, electric fields of up to 
300 kilovolts per meter can be 
created. What is the cause of such 
fields? In the case of the super- 
tankers that is not merely an aca- 
demic question, for there have been 
several large explosions during the 
cleaning of those ships. 

539; 1296; 7307 through 1311. 


Happiness and negative charge 

It is thought that if you enter a 
negatively charged atmosphere, 
such as the bathroom discussed 
above, a feeling of well-being will 
come over you. Being charged 
negatively makes you happy; 
being charged positively makes 
you ill at ease. So, perhaps your 
feeling good after a shower has as 
much to do with the negative 
charge in the bathroom as with 
feeling clean. Can you explain 
why negative and positive charge 
might affect you this way?* 

1307; 1408. 

*Also see Prob. 3.18 on the Chinook, 

The electrician's evil and the rings magic 155 


Fall through the floor 

Why don't you fall through the 
floor? Fundamentally, what sup- 
ports you? 


Sand castles and crumbs 

If you want to make a sand castle 
at the beach, you use wet sand, not 
dry. Common table salt shows the 
same tendency to be much more 
cohesive when wet. Other powders 
such as cocoa and chalk, however, 
are cohesive even when dry. What 
forces are responsible for the 
cohesiveness of a powder? Why 
does it matter whether a powder 
such as sand or salt is wet? Do 
you think a fine powder should be 
more or less cohesive than a coarse 

Crumb formation is essential for 
maintaining a fertile soil, yet if 
the soil is misused, a useless dust 
ball may develop. What is respon- 
sible for crumb formation in soil? 
Why don't other things, such as 
sand and face powder, form 

1313, pp. 288-290; 1314; 1315. 


Food wrap 

Some clear food wraps can be 
tightly stretched over a container 
and folded down the sides, and 
they will retain the tension and 
completely secure the container. 
The food wraps "stick." How do 
they do this? 


(6.19 through 6.24) 


Magnetic-field dollar bill 

If you hang a dollar bill from one 
end and bring a large magnet (with 
a nonuniform field) toward it, the 
bill will move toward one of the 
pole faces. Why? 



Bubbles moved by magnetic field 

A large magnet placed near a 
carpenter's bubble level will force 
the bubble to move. How does 
the magnetic field do that? Does 
the bubble move toward or away 
from the magnet? 




Electromagnetic levitation 

You can levitate a metal ring on a 
coil through which a steady AC cur- 
rent passes (Figure 6.21 ), but if the 
current is quickly turned on, the 
ring will jump into the air very 
dramatically. Why is there a dif- 
ference in behavior in these two 
cases? What supports the ring 
against gravitation when it is being 
levitated, and what determines 
the height at which it floats? 
How stable is the levitation (does 

the ring sit against the pole and at 
a tilt)? In predicting the behavior 
of various rings, your intuition 
may fail. So, for fun, first try to 
guess what will happen in the 
following circumstances and then 
actually see what does happen. 
Will a thin ring float at the same 
height as a thicker ring if the 
density and diameter are the same? 
What happens should both rings 
be on the coil when the current 
is slowly increased? Finally, what 
happens if one of the rings is 
wider than the other? 

1317 through 1321. 

Figure 6.21 

Metal ring suspended on coil 



Turning in the shade of a magnetic 

Can partially shading a magnetic 
field from a copper disc cause the 
disc to rotate? Over one of the 
poles on an alternating magnet, 
place a copper disc that is free to 
rotate (Figure 6.22). The disc is 
repelled hut shows no desire to 
rotate. But now insert another 
copper sheet between the disc 

156 The flying circus of physics 

Copper sheet 


Figure 6.22 

Disc rotates when the copper 

sheet partially shields it. 

and the magnet, partially shading 
the disc from the magnetic field. 
Immediately the disc begins to 
turn. Can you explain why? 

1321, pp. 82 ff. 



Car speedometer 

Will a horseshoe magnet attract 
aluminum? No, normally it won't. 
(Why not?) There is a special ar- 
rangement, however, in which a 
magnet will move aluminum. 
Suspend a horseshoe magnet on a 
string above an aluminum disc 

Figure 6.23 

Aluminum disc turns under- 
neath turning magnet. 

(Figure 6.23). Somehow suspend 
the disc so that it's free to rotate 
about its center. If the magnet is 
set spinning, the disc will spin also. 
Will the disc turn in the same sense 
as the magnet? Why is aluminum 
only affected in this case? 

This is basically how your car's 
speedometer works, except that 
in your car the rotating magnet 
is inside an aluminum can to which 
a pointer is attached and the can 
is restrained by a spring. 

155, p. 344; 592, p. 87. 


Figure 6.24 

Ball undergoes perpetual motion. 


Perpetual magnetic motion 

Of the many fascinating perpetual 
machines proposed through 
history,* that of the Bishop of 
Chester (1670s) is one of the 
simplest (Figure 6.24). The mag- 
net that was fixed on the column 
was to draw the iron ball up the 
ramp until the ball reached the 
hole in the ramp. The ball would 
then fall and be returned to the 
ramp's base, and the procedure 
would begin again. Very straight- 
forward, right? Shouldn't it work? 

*See Refs. 1322 through 1324. 

Radio and 



(6.25 through 6.31) 

ionospheric physics 

plasma frequency 

electromagnetic waves 


Radio, TV reception range 

There are several things about radio 
that have always puzzled me. For 
example, why can AM stations be 
received at night over a much larger 
range than during the day? Some- 
times you can pick up a station 
halfway across the United States 
on a cheap transistor radio. (One 
consequence of this is that the FCC 
requires most AM stations to cut 
their power or even to leave the air 
at dusk.) When Marconi transmitted 
the first wireless signals across the 
Atlantic, many people were amazed. 
Why didn't those signals go directly 
into space instead of following the 
curving surface of the earth as they 

FM and TV stations, however, 
hardly even get their reception 
areas out of the city. Occasionally, 
such as during a meteor shower, 
these signals do travel surprising 
distances; at other times, such as 
during major solar flares, they 
are tremendously reduced, world- 
wide communication being almost 
destroyed. First, why is there such 
a difference between the ranges of 
TV and FM on one hand and AM 
on the other? Next, why are there 

The electricians evil and the rings magic 157 

occasionally such dramatic changes 
in the transmission ranges of TV 

170, pp. 138- 139; 215, pp. 43 ff; 
1326; 1327. 



Crystal radio 

The crystal radio of my boyhood 
was very simple, being only an 
antenna wire, a capacitor, a long 
wire coil, earphones, and finally, 
a crystal (Figure 6.26). Do you 
understand how it worked? For 
example, why did moving the 
contact on the wire coil change 
stations? Why was the crystal 

Every now and then there are 
stories about people who can hear 


Figure 6.26 
Crystal radio. 

local radio stations on their teeth 
fillings, on their bedsprings, etc. 
Could there be any truth to these 
stories? If so, then what is it in 
these strange radio sets that is 
taking the place of the crystal in 
the crystal set? 

158, pp. 577-578; 21 1, pp. 417- 
418; 253, p. 409. 


Airplane interference with TV 

How does a nearby airplane inter- 
fere with your TV picture? 


AM car antenna 

Why are AM radio antennas mount- 
ed outside a car and usually ver- 
tically? How much does it matter 
if they are mounted in the wind- 
shield glass? 


Multiple stations on radio 

Normally I hear one local station 
for a given setting on my car radio. 
Yet when I drive near a radio sta- 
tion's antenna, I can sometimes hear 
that station plus another for one 
setting. Why? Sometimes I can 
even get one station at many settings 
of my radio dial. Again, why? 

charged particles in magnetic field 

atomic and molecular excitation 


Auroral displays 

"After darkness has fallen, 
a faint arc of light may 
sooner or later be seen low 
on the north horizon, or 
centered somewhat to 
the east of north. Gradual- 
ly it rises in the sky, and 
grows in brightness. As 
it mounts in the sky, its 
ends, on the horizon, 
advance to the east and 
west. Its light is a trans- 
parent white when faint, 
and commonly pale 
yellow-green when bright— 
rather like the tender 
color of a young plant 
that germinates in the 
dark. The breadth of 
the arc is perhaps thrice 
that of a rainbow. The 
lower edge is generally 
more definite than the 
upper. The motion up- 
ward toward the zenith 
may be so slow that the 
scene is one of repose. 
As the arc rises, another 
may appear beyond it, 
and follow its rise. At 
times four, five, or even 
more arcs may thus 
appear. They rise together, 
and some of them may 
cross the zenith and pass 
onwards into the southern 
half of the sky. 

158 The flying circus of physics 

Figure 6. 30 

"But we went to see the northern lights last week. " (Chicago 

Tribune Magaz ine.) 

"This may be all that 
appears on some nights. 
But on others the aurora 
enters after a while on a 
new and distinctly dif- 
ferent phase, much more 
active and varied. The 
transition from the quiet 
to the active phase may 
be speedy, even sudden. 
The band becomes thinner, 
rays appear in it, it begins 
to fold and also to become 
corrugated in finer pleats. 
It becomes a rayed band of 
irregular changing form, 
like a great curtain of drap- 
ery in the sky. Its color 
may remain yellow-green, 
but often a purplish-red 
border appears along the 
lower edge, perhaps inter- 
mittently. Vivid green or 
violet or blue colors some- 
times appear. At times 
the rays seem to be dart- 
ing down, like spears shot 
from above. Sometimes 

there seems to be an up- 
ward motion along the 
rays, or motion to the east 
or west along the band. 
The curtains may sweep 
rapidly across the sky as 
if they were the sport of 
breezes in the high air; or 
they may vanish and re- 
appear, in the same place 
or elsewhere. This grand 
display may continue for 
many minutes or even 
hours, incessantly chang- 
ing in form, location, 
color and intensity; or 
intermissions may occur, 
when the sky has little 
or no aurora. 

"At times the observer 
may look up into a great 
auroral fold nearly over- 
head, when the rays in 
its different parts will 
seem to converge, form- 
ing what is called a 
corona or crown. Often 
such a corona rapidly 

fluctuates in form, and 
its rays may flash and 
flare on all sides, or 
roll around the center. 

"At the end of an out- 
standing display the aurora 
may assume fantastic forms, 
no longer in connected 
curtains and bands. There 
may be a widespread col- 
lection of small curtains, 
stretching over a large 
part of the sky, which 
brighten and fade, or, as 
it is said, pulsate. Finally, 
the sky may be covered 
by soft billowy clouds, 
not unlike a mackerel 
sky with rather large 
"scales"; but these 
"scales" and patches 
appear and disappear, 
with periods of not 
many seconds. At last 
the sky becomes altogether 
clear, with no more aurora. 
But later the whole se- 
quence may begin anew, 
and continue till dawn 
pales the soft auroral 
light (1328)." 

Explaining the aurora in detail is 
still a matter of current research, 
but can you explain in general why 
the aurora is formed and why some 
of these colors and wavelike struc- 
tures appear? Why are auroral 
displays so much more frequent at 
high latitudes? Why are there more 
displays over northern Canada than, 
for example, over Siberia at the 
same (geographical) latitude? 

219, pp. 242-246; 1328; 1329. 

The electrician's evil and the rings magic 159 





In World War I the Germans eaves- 
dropped on Allied field telephone 
messages by detecting the small 
leakage from the telephone wires 
into the ground. The initial pickup 
was by two metallic probes driven 
into the ground a couple hundred 
yards apart and at some distance 
from the telephone wires. Once the 
signals were fed into a high-gain 
amplifier, they became audible to 
the German intelligence personnel. 
But during such monitorings, the 
Germans also heard mysterious, 
relatively strong whistlings whose 
pitch would steadily fall. These 
sounds have since been associated 
with ionospheric phenomena ap- 
propriately called "whistlers" and 
other sounds such as clicks, tweeks, 
chinks, and a whistling of rapidly 
rising pitch called the "dawn 
chorus" have been detected. Can 
you explain the sources of these 

2 19, pp. 302-304; 1330; 1331. 


(6.32 through 6.49) 


electric field 

electric potential 



Lightning is so familiar that its 
beauty runs the risk of being 
overlooked. So, before we get into 
some of the strange or paradoxical 
features of lightning, let's ask some 
simple questions about its com- 
mon properties. In a lightning dis- 
charge there are a t least two strokes: 
usually there is first a "leader," 
then a "return." Which do you see, 
and why don't you see both?f 
Why do you even see one- what 
produces the visible light? 
Does the visible stroke go up or 
down? Why is it so crooked? 
How much current is involved in a 
flash? How bright is a flash? Ap- 
proximately how wide is the light- 
ning channel you see ? One hundred 
meters? One meter? Several milli- 
meters? How long does the flash 
last? Several seconds? Several 
milliseconds? A microsecond or so? 

220; 299, pp. 110-123,300; 
301; 332, Vol. II, Chapter 9; 
1332; 1333; 1550; 1590. 

"Suggestions for photographing light- 
ning flashes are given by Orville (1 334). 
The first lightning photograph ever taken 
is reproduced in Jennings (1335). 

1" If you are driving through rain at 
night, a muitiple-flash stroke can give 
several stroboscopic images of your 
moving windshield wiper (1336). 


Earth's field 

The big question, however, is why 
there is lightning at all? What is 
responsible for the electric field 
that is between the earth's surface 
and the clouds? Outdoors there is 
a 200-volt difference between the 
heights of you nose and feet. Why 
aren't you shocked by that voltage 
difference (Figure 6.33)? Can 
motors be driven by this electric 
field? In some cases, yes. 

299, pp. 97-109; 300, pp. 105- 
106; 332, Vol. II, Chapter 9; 
1296; 1337 through 1339; 1548; 
1549; 1568. 

"Goodness, did you know there's 
a 200 volt difference between 
the heights of your nose and 
your feet? How is it that we 
don't get shocked?" 

Figure 6.33 

The earth's electric field. 

160 The flying circus of physics 

Figure 6.34a 
Cloud-to-air stroke. 


Lightning forms 

The cloud- to-ground lightning 
stroke is not the only type of 
lightning. The cloud-to-air 
stroke, for example, termin- 
ates in midair (Figure 6.34a). 
If the cloud is too distant to be 
seen, you may suddenly be awed 
by such a "bolt from the blue." 
Under some circumstances you 

Figure 6 34b 
Ribbon lightning. 

will see several parallel strokes 
that give the impression of a 
ribbon hanging from the clouds 
(Figure 6.34/?) The most exciting 
stroke, however, is probably 
"bead lightning" (Figure 6.34c), 
which appears to be a series of 
brilliant beads tied to a crooked 
string. In these several examples 

Figure 6.34c 
Bead lightning. 

what causes the strokes or the 
special appearance of the strokes? 
In the cloud-to-air case, where 
does the current of the discharge 

299, pp. 128- 129; 300, p. 5; 
301, p. 45; 1340; 1341; 1611, 
Section GL; 1623. 


Ball lightning 

One of the most controversial sub- 
jects in physics is whether or not 
ball lightning exists. This argument 
persists in spite of the enormous 
number of sightings and many 
published accounts. Perhaps as 
much as 5 percent of the world's 
population have seen it (1350, 
1351), yet many will argue 
vigorously that it is an illusion, such 
as an afterimage resulting from 
having seen a bright flash of light. 
The luminous, silent balls of light 

reportedly float through the air 
or slowly dance about for several 
seconds. They can sometimes pass 
through window glass without a 
trace of damage; at other times, 
the glass is shattered. They are 
seen in all manner of structures 
(even in metal airplanes) as well as 
outdoors. Though they are usually 
silent, their demise is accompanied 
with a pop. Finally, they are dead- 
ly. G. W. Richmann was apparently 
a victim while trying to repeat the 
results of Franklin's kite experi- 
ment. A pale blue fireball about 
the size of a fist left the lightning 
rod in his lab, floated quietly to 

Richmann's face, and exploded. 
With a red spot on his forehead and 
two holes in one of his shoes, 
Richmann was left dead on the 

In reviewing the many explana- 
tions of ball lightning, can you 
identify those with any real pos- 
sibility of being correct? Can you 
also devise other explanations or 
argue that ball lightning can only 
be an illusion? 

299; pp. 130-133; 1349 
through 1370; 161 1, Section 

The electrician's evil and the rings magic 161 

Figure 6.36 


H-bomb lightning 

Lightning flashes were also photo- 
graphed surrounding another 
catastrophic event, the fireball 
of the 10-megaton thermonuclear 
device triggered in 1 952 at Eniwe- 
tok Atoll. The strokes propagated 
upward from the surface of the 
sea, and the branching was also 
upward (Figure 6.36). As the fire- 
ball expanded and reached the 
points where the lightning channels 
were previously visible (the visible 
flashes had disappeared by then), 

the tortuous channels were again 
visible against the backdrop of 
the fireball. The charge produc- 
tion for the lightning must have 
been set up very rapidly, but 
precisely what caused it is still 
not well known. Can you suggest 
possible explanations? Can you 
also explain why the channels 
became visible again against the 
fireball background? 

1347; 1348. 


Volcanic lightning 

When the volcano that formed the 
new islet, Surtsey, rose furiously 
from the Icelandic sea in 1963, 
brilliant lightning displays danced 
in the volcano's dark clouds. What 
provided the tremendous charging 
for the lightning? One possible 
mechansim was sea water striking 
the molten lava. How would that 
produce the charge? 

1342 through 1346. 


Earthquake lightning 

Should an earthquake produce 
lightning discharges? The Japanese 
have learned that lightning dis- 
charges in a clear sky are signs of 
impending earthquakes. Indeed, 
earthquakes there and in other areas 
are sometimes associated with both 
normal lightning and ball lightning. 
Why should there be any connection 
between the two phenomena? 

1371; 1372. 


Franklin's kite 

Benjamin Franklin's kite experi- 
ment was probably first introduced 
to you somewhere in elementary 
school, but do you understand all 
the little points about what Franklin 
did, and why he was not killed? 
The following is Franklin's letter 
to a friend describing the experi- 

To the top of the upright 

stick of the [kite's] cross 

is to be fixed a very sharp 

pointed wire, rising a foot 

or more above the wood. 

To the end of the twine, 

next the hand, is to be 

tied a silk ribbon, and 

where the silk and twine 

join, a key may be fas- 
tened. This kite is to be 

raised when a thunder 

gust appears to be 

coming on, and the person 

who holds the string must 

stand within a door or 

window or under some 

cover, so that the silk 

ribbon may not be wet; 

and care must be taken 

that the twine does not 

touch the frame of the 

door or window. As soon 

as any of the thunder 

clouds come over the 

kite, the pointed wire 

will draw the electric 

fire from them, and the 

kite, with all the twine, 

will be electrified, and 

the loose filaments of 

the twine will stand out 

162 The flying circus of physics 

every way, and be at- 
tracted by an approach- 
ing finger. And when 
the rain has wet the kite 
and twine, so that it can 
conduct the electric fire 
freely, you will find it 
stream out plentifully 
from the key on the ap- 
proach of your knuckle. 
At the key the phial* may 
be charged, and from elec- 
tric fire thus obtained, 
spirits may be kindled, and 
all the other electric experi- 
ments be performed, which 
are usually done by the help 
of the rubbed globe or tube, 
and thereby the sameness 
of the electric matter with 
that of lightning completely 

Why did he put a pointed wire on 
the kite's top? Why the silk ribbon 
between the key and his hand? 
Why the key? Why was the twine 
attracted to his finger, and why 
did loose filaments stand out? 
What caused the light emission he 
saw when his knuckle was brought 
close to the key? Why wasn't 
Franklin killed? If a lightning 
stroke had hit the kite or string, 
would he have survived? In Europe 
G. W. Richmann was killed in trying 
to repeat the Franklin experimentst 
so don't you try it, even with 
Franklin's precautions. 

299, pp. 37-44; 30 1, Chapter 2; 
1373; 1374. 

*An early form of capacitor. 
f See Prob. 6.35. 


Lightning rod 

My grandmother's lightning rod 
has a sharp point, stands several 
feet taller than the house, and is 
buried several feet into the ground. 
Why are those features desirable? 
What is the rod really supposed to 
accomplish? There has been con- 
siderable debate over this question 
ever since Benjamin Franklin's 
invention of the lightning rod. 
Some claim that the rod helps dis- 
charge a cloud as it passes over- 
head, thereby avoiding the cata- 
strophic breakdown of lightning. 
Others claim that the rod merely 
provides a safe route to ground 
for any flash near the rod. 

There have also been many mis- 
conceptions and controversies 
about the performance and in- 
stallation of lightning rods. For a 
while after their first introduction, 
strong arguments were made for a 
top with a round metal knob or 
even a glass knob. Convincing 
arguments were also made that the 
lower part should be attached to 
the top soil only, for an explosion 
could occur if the flash were car- 
ried deep into moist ground. Re- 
cently a company was fitting its 
rods with a radioactive source at 
top. That source was to aid in 
ionizing the air, thereby further 
seducing the flash to strike the 
rod rather than the protected 
building. Would a radioactive 
source really be of any aid? 

299 ', pp. 188 ff; 300, Chapter 15; 
301, Chapters 2, 6; 1296; 1373 
through 1381. 


Lightning and trees 

There's an old wives tale about 
lightning seeking out oak trees. In 
fact, a strikingly high proportion of 
trees shattered by lightning are oaks. 
It is hard to believe, however, that 
lightning knows the difference be- 
tween an oak and any other type 
of tree. Why then is there such 
preferential shattering? How ex- 
actly does the lightning stroke make 
a tree explode, anyway? Of course, 
a strike does not always result in an 
explosion. For example, Orville 
(1389, 1390) has published a re- 
markable photograph of a direct 
hit sustained by a European ash 
tree. Upon close examination the 
following day, the tree bore no in- 
dication of its experience. 

How does lightning start forest 
fires? Why aren't fires started in all 
lightning strikes in wooded areas? 

299, pp. 177-187; 300, p. 151; 
301, p. 60; 1382 through 1390. 


Lightning strikes to aircraft 

Lightning strikes to aircraft are 
frequent, but it is very rare that 
there is any damage other than 
perhaps several tiny holes in the 
fuselage. Cars, buses, and other 
such vehicles also enjoy immunity 
from damage. Soon after lift-off 
Apollo 12 was struck twice by 

The electricians evil and the rings magic 163 

lightning with no apparent ill ef- 
fects to the spacecraft or its crew. 
In each of these cases why is there 
no damage to the vehicle or injury 
to the occupants? Indeed, the 
occupants may never even be 
aware of the strike.* 

299, pp. 232-235, 249 ff; 300, 
pp. 151-152; 301, pp. 51-54; 
1296; 1379; 1391, p. 22; 1392 
through 1397. 

*An alert airplane passenger may foresee 
a lightning strike by noticing a sudden 
increase in St. Elmo's fire (see Prob. 
6.47) on the wing tips and other pointed 
objects. The luminous streamers may 
be 10 or 15 feet long and half a foot 
wide (301). 


Rain gush after lightning 

Perhaps you have noticed sudden 
gushes of rain or hail moments 
after lightning strokes in thunder- 
storms. Is there any connection 
between the gush and the stroke or 
the thunder? Or is this just a coin- 

164, pp. 358-359; 300, pp. 165- 
166; 301, p. 152; 1398 through 
1400; 1619. 


Clothes thrown off 

If you're struck by lightning, you 
may very well have your clothing 
and shoes thrown off. What causes 

301, p. 131. 


Ground fields in lightning hit 

If you are caught in a thunder- 
storm you should not stand under 
a tree, and you should keep your 
head lower than your surroundings. 
Why is the tree dangerous? As 
long as you stand away from the 
trunk, aren't you safe enough? 

Should you ever lie down? That 
would give your head the minimum 
possible elevation, but is there any 
additional danger encountered in 
lying down? Cows are often killed 

or hurt by lightning. Not only do 
they commonly stay outdoors and 
often seek shelter under trees, but 
the separation of their hind legs 
from their front legs increases the 
danger (Figure 6.45). They are 
thus similar to a man lying down. 
Again, why is this dangerous? 

299, p. 223; 301, pp. 61-64; 
1350, p. 279; 1391, pp. 282- 

., '^M****-**"*'' ^r / / 


Figure 6.45 

Why will the cow be killed even through the lightning has struck 
something else? (Figure from Lightning Protection for Electric 
Systems by Edward Beck, published by McGraw-Hill). 

164 The flying circus of physics 


St. Elmo's fire 

St. Elmo's fire is a fairly con- 
tinuous luminous discharge seen 
from such things as masts of 
ships, wing tips of airplanes, and 
even bushes. There is a crackling 
noise associated with the blue, 
green, or violet color of the light. 
Can you explain, first of all, 
what causes this light, and second, 
why those particular colors? 
A favorite stunt of mountain 
guides, when the air is 
throughly charged, is to imi- 
tate Thor by waving an ice- 
axe over their heads. The 
metal parts of the ice-axe 
draw down an impressive 
display of electrical poly- 
technics. A geological ham- 
mer will sometimes spit long 
hot sparks in one position, 
but if the head is turned 
at right angles to the former 
position, the sparking 
stops. . . They usually de- 
tect charged air by raising 
a finger above their heads. 
When the air is heavily 
charged, sparks will sizzle 
from the fingertip, making 
a noise like frying bacon (354). 
Another example, somewhat dif- 
ferent in appearance, is the electric 
sparks, several meters long, which 
may spring up from the tops of 
sand dunes during thunderstorms. 
In this case, the blowing sand must 
contibute to the sparking, but how? 

165, p. 233; 301, pp. 47-50; 
354, p. 744; 961; 1402, p. 2 19; 


Living through lightning 

There are many cases of people 
living through direct and indirect 
lightning hits. There are even 
cases where the lightning has 
stopped a person's breathing for 
perhaps 20 minutes, yet the per- 
son has fully recovered with no 
apparent brain damage due to 
electrical shock or oxygen starva- 
tion. It has been suggested (1401 ) 
that such a shock momentarily 
changes the brain's crucial need 
for oxygen. In any case, shouldn't 
the victim be severely burned and 
his heartbeat halted? How much 
energy (or power) is deposited in 
such a victim? 

299, pp. 226-230; 301, p. 131; 


Andes glow 

Single flashes of light and con- 
tinuous glows can he seen over the 
peaks of certain mountain ranges. 
They have been described as "not 
only clothing the peaks, but 
producing great beams, which can 
be seen miles out to sea" (1404). 
Generally these mysterious lights 
are called Andes glow, though 
this doesn't mean they are re- 
stricted to the Andes. What 
causes this glow? St. Elmo's fire 
from many points on a peak? 
St. Elmo's fire is usually only a 
few centimeters long, so how 
could it be seen miles away? 

165, p. 233; 1404 through 1406. 


Electrical pinwheel 

A demonstration sometimes seen 
in physics classes involves a pin- 
wheel that is made to rotate by a 
high DC voltage (Figure 6.49). 
Why this happens was a point of 
controversy over the last two cen- 
turies, but recently the device has 
been somewhat neglected. Does 
the pinwheel turn because of 
something that it throws off or 
pulls on or for some other reason? 
Will it work in a vacuum or in a 
dusWree environment? Why does 
the color of the discharge depend 
on the polarity of the pinwheel? 
Why do the tips need to be sharp? 
Finally, can you calculate how 
fast the pinwheel will turn under 
given conditions?* 

155, pp. 434-435; 1407. 

*Also see Prob. 6.33. 

High-voltage source 

Figure 6.49 

Rotating pinwheel driven by 

electrical discharge. 

The electrician's evil and the rings magic 165 


Power-line blues 

In order to transmit electrical 
power more efficiently, some 
electrical companies have erected 
"extra-high-voltage" (765,000 
volt) transmission lines. Such 
lines may be beneficial on the 
whole, but they have worried those 
people living near the lines. Dis- 
turbingly, the lines often glow an 
erie blue and can cause disconnected 
fluorescent tubes to light mysterious 

ly. More threatening, however, is 
that numerous people have received 
shocks when touching metallic ob- 
jects in the vicinity of the extra- 
high-voltage lines. 
In a recent survey, 18 families 
living near Ohio Power Co.'s 
line reported being shocked 
by touching farm machinery, 
wire fences or even damp 
clotheslines. Two women 
complained of shocks received 
while on the toilet. Other 
complaints were bad TV re- 
ception and the sizzling 

sound of the electrical dis- 
charge. Said C. B. Ruggles, 
whose farm is split by the 
line: "You'd swear we 
were living near a waterfall" 
How would a powerline such as 
this cause objects in its vicinity to 
give shocks? I have heard that 
some people run electrical motors 
by connecting them to antennas 
surreptitiously buried near the 
power lines. Is it possible to get 
power this way? 


1 66 The flying circus of physics 

The walrus has his 
last say and leaves 
us assorted goodies 

«f£^— - 


UFO propulsion 

When "your gravity fails 

and negativity don't pull 

you through." 

---Bob Dylan, "Just Like 

Tom Thumb's Blues"* 

In light of physical laws, let's 
reconsider the possibility that the 
UFOs sighted during the last few 
decades are intelligently controlled 
craft. Consider the method of 
propulsion, for instance. No local 
destruction has ever been noted at 
the site of a landing or lift-off. 
For objects as large as space 
ships, is this possible with any kind 
of chemical or nuclear power? How 
much energy would be involved 
with those sources? Could the 
vehicle somehow use the earth's 
electric or magnetic field? If so, 
how much acceleration would be 
possible, and would there be an 
altitude limitation? 

One of the most popular pro- 
pulsion mechanisms in science fic- 
tion has been gravitational shield- 
ing. H. G. Wells used it long ago 
to get men to the moon. Suppose 
a craft could suddenly shield it- 
self from the earth's gravitational 
field. Would it lift off? If it did, 
how fast would it move? In par- 
ticular, would it move at anywhere 
near the fast speeds reported for 


*© 1965 M. Witmark & Sons, All 
rights- reserved, Used by permission 


Violating the virgin sky 

Cyrano de Bergerac uses the most 
incredible physics ever recorded 
to keep the villainous de Guiche 
from Roxanne's house while she is 
being married. Dropping from a 
branch into de Guiche's path, 
Cyrano swears he has just fallen 
from the moon. 
CYRANO: From the moon, 
the moon! I fell out of the 
DE GUICHE: The fellow 
is mad— 

CYRANO (Rapidly): 
You wish to know by 
what mysterious 
I reached the moon? 

I myself 

Discovered not one 
scheme merely, but six- 
Six ways to violate the 
virgin sky! 
(De Guiche has succeeded 
in passing him, and moves 

toward the door of Rox- 
anne's house. Cyrano 
follows, ready to use 
violence if necessary.) 
around.): Six? 
CYRANO (With increasing 

As for instance— Having 

stripped myself 

Bare as a wax candle, 

adorn my form 

With Crystal vials filled 

with morning dew, 

And so be drawn aloft, 

as the sun rises 

Drinking the mist of dawn! 
DE GUICHE (Takes a step 
toward Cyrano.): 

Yes— that makes one. 
CYRANO (Draws back to 
lead him away from the 
door; speaks faster and 

Or, sealing up the air 

in a cedar chest, 

Rarefy it by means 

of mirrors, placed 

In an icosadedron. 
DE GUICHE (Takes another 
step.): Two. 

Figure 7.2 
Self-motivation (Goofy, 

'Victory Vehicles, " © Walt Disney ProdJ. 

168 The flying circus of physics 

CYRANO (Still retreating): 

I might construct a 
rocket, in the form 
Of a huge locust, driven 
by impulses 
Of villainous saltpetre 
from the rear, 
Upward, by leaps and 
DE GUICHE (Interested in 
spite of himself, and count- 
ing on his fingers.): 

CYRANO (Same business): 
Or again, 

Smoke having a natural 
tendency to rise, 
Blow in a globe enough 
to raise me. 
DE GUICHE (Same busi- 
ness, more and more as- 
tonished.): Four! 
CYRANO: Or since Diana, 
as old fables tell, 
Draws forth to fill her 
crescent horn, the mar- 

Of bulls and goats— to 
anoint myself there- 
DE GUICHE (Hypnotized): 

CYRANO (Has by this time 
led him all the way across 
the street, close to a 
Finally— seated on an 
iron plate, 
To hurl a magnet in 
the air— the iron 
Follows— I catch the 
magnet— throw again— 
And so proceed in- 

All excellent,— and 
which did you adopt? 

CYRANO (Coolly): Why 
none of them. . .A seventh. 

The ocean!. . . 

What hour its rising 

tide seeks the full 


I laid me on the strand, 

fresh from the spray, 

My head fronting the 

moonbeams, since the 


Retains moisture— and 

so I slowly rose 

As upon angel's wings, 

effortlessly, Upward.* 

*From Cyrano de Bergerac by Edmond 
Rostand, translated by Brian Hooker, 
published by Holt, Rinehart and Winston, 



Olbers' paradox 

Some have argued that the 
universe is infinitely large and 
contains an infinite number of 
stars. Olbers' paradox is that 
"if the universe is infinite in 
extent and contains an infinite 
number of stars evenly distributed, 
the sky should be blazing all over 
in brilliant light" (1414). Of 
course, the intensity of the light 
from distant stars will be less than 
from nearby stars. But if the stars 
are evenly distributed, then their 
number increases with distance 
from the earth just enough to 


Figure 7.3 

"Vm not sure, but it looks like 

in fin ity. ' ' (Ph i De Ita Kappan. ) 

balance the decrease in light in- 
tensity from each star. Hence, the 
total light coming from any given 
distance should be the same as 
from any other distance. With an 
infinite number of stars, the night- 
time sky should be bright and 
evenly lit. Why, instead, is the 
nighttime sky relatively dark? 

1410 through 1416; 1587. 

atmospheric physics 

gravity waves 


Noctilucent clouds 

Shortly after a summer sunset 
in the high latitudes, ghostly, 
silvery-blue clouds may appear 
against the dark sky. They are 
called noctilucent clouds (lu- 

The walrus has his last say and leaves us assorted goodies 169 

minous night clouds), and their 
origin is still highly controver- 
sial. They may be associated 
with extraterrestrial dust entering 
the atmosphere, but this has not 
yet been proved. Why are they 
visible only after sunset? Since 
they are seen when the sky is 
dark, about how high are they? 
Why are they usually seen only 
in the high latitudes and only in 
the summer? Why do they often 
appear in a wavy pattern, as 
though the clouds were the surface 
of a sea? 

362, pp. 150-151; 954, pp. 
284-287; 1417 through 1423. 


Water witching 

Some people claim they can locate 
underground water by walking over 
the area with a forked stick, rod, 
or something similar (Figure 7.5a). 
When directly over water the in- 
strument reportedly dips to indicate 
the (unseen) water (Figure 7.5b). 

Figure 7.5a 

A water witch's forked stick. 

ABOUT 6ETT\H& *&r\ 

Figure 7.5b 

(By permission of John Hart. 

Field Enterprises.) 

This procedure -called dowsing, 
water witching, or divining- is con- 
troversial: there are many success 
stories on the one hand but a com- 
plete absence of explanation in 
physical terms on the other. What 
could possibly be the force that 
influences either the instrument 
itself or the person holding it? Is 
there some clue, perhaps even a 
subconscious one, that tips off 
the water witch to the presence of 

1520 through 1523. 

shock waves 

energy transfer 


Snow waves 

A footstep in a field of snow may 
set off a snowquake that propagates 
away from the site and causes a 
lowering of the snow level and a 
swishing sound. If the disturbance 
encounters a barren area, it will be 
reflected back through its origin, 
and the swishing of the second pas- 
sage can be heard. What causes 
these snowquakes to propagate, 
and what determines their speed? 
Why does their passage lower the 
snow level and cause a swishing 
sound? Finally, why will a barren 
area reflect them? 

1426; 1427; 1455. 


Fixed-point theorem 

If you stir a cup of coffee and then 
let it come to rest, at least one 
point on the coffee's surface will 
be back in its original place. (The 
stirring must be smooth, with no 
splashing.) If you were to rip out 
this page, crumple it, wad it, and 
then lay the wadded ball back in 
the book, at least one point on 
the page will be directly over its 
original position. Why is this 
guaranteed in these two cases 
every time? 

1428 through 1430. 

170 The flying circus of physics 

Figure 7.8 

Should we worry about a geophysical weapons gap? 


The great leap downward 

The Republic of China commands 
an awesome new weapon— a geo- 
physical weapon. It has been sug- 
gested that should all of its 750 
million people leap simultaneously 
from 6 1/2-foot-high platforms, 
they would set up shock waves in 
the earth. By jumping again each 
time the shock waves pass through 
China, the Chinese could build the 
waves up to the point that they 
could destroy parts of the United 

States, especially California, which 
is already endangered by earth- 

What path would such a shock 
wave take through the earth? How 
frequently should the Chinese jump 
to amplify the wave, and how much 
energy is added to it by each jump? 
Is there any way another country's 
population could defend itself 
against this geophysical weapon, 

for example, by some appropriate 
type of retaliatory jumping (Fig- 
ure 7.8)? Does it matter how 
the Chinese jump? For example, 
one writer has argued it is essential 
the Chinese jump with stiff knees, 
for bent-knee jumping would im- 
part far less energy to the ground. 
Is that true? 

1424; 1425. 


Beating and heating egg whites 

Why does beating egg whites 
change them from a fluid to a 
thick foam? For instance, in 
making meringues the egg whites 
are beaten until they peak, (when 
the beater is lifted out, the sub- 
stance is stiff enough that it is 

left in a peak). What does the 
beating do to the egg white to 
cause it to stiffen? Similarly, what 
is physically responsible for 
transforming the egg white— initial- 
ly a colorless, transparent fluid— into 
a white solid when, for example, you 
fry an egg? 

316, pp. 123-126,87-90; 1431. 

Scotch tape rheology 



Pulling off Scotch tape 

Scotch tape cannot really get into 
the surface irregularities of what- 
ever it is being applied to, yet it 
holds well when you try to peel it 
off. The adhesion is partly due to 

The walrus has his last say and leaves us assorted goodies 171 



Figure 7.10 

Compression point in tape being 

pulled upward. 

a line of compression that runs 
ahead of the line of separation as 
you peel the tape (Figure 7.10). 
The line of compression can be 
seen if you stick two tape strips 
together and slowly separate them. 
What causes the compression? 

950; 1432. 



Footprints in the sand 

Have you ever strolled along the 
beach as the water was receding? 
As you step onto the firm sand, 
the sand around your foot im- 
mediately dries out and turns white. 
The popular explanation for the 
whitening is that the water is 
squeezed out of the sand by your 
weight. That, however, is not the 
case, because sand does not behave 
at all like a sponge. So, what does 
cause the whitening? Does it last 
as long as you stand there? 

924, p. 373; 937; 938; 1313, 
pp. 288-294; 1433, pp. 624- 
626; 1434; 1435. 



Balloon filled with water and sand 

Partially fill a rubber balloon with 
sand and water so there is 
more than enough water to cover 
the sand but not enough to fill the 
entire balloon. Then tie up the top 
and try squeezing the balloon. 
Pretty easy at first, isn't it? As you 
continue to compress the balloon, 
however, you'll suddenly find a 
point where the balloon just refuses 
to bulge even though you squeeze 
for all you're worth. What causes 
this sudden and determined resis- 
tance to further squeezing? 

924, p. 373; 938; 1313, pp. 
288-294; 1433, pp. 624-626; 
1434; 1435. 


Buying a sack of corn 

In the days when shucked corn 
was sold by volume rather than by 
weight, vendors would make the 
corn assume as much volume as 
possible. Hence, a bag of corn, 
while appearing full, may have 
had less corn in it than another 
bag of the same size sold by a 
more-honest merchant. Faced 
with this problem, should the 
buyer have tried to press a bag so 
as to make the corn denser? Does 
the corn's volume decrease if you 
press on the bag? Actually, press- 
ing is exactly the wrong thing to 
do. Why? 

938; 1433, pp. 624-626; 1434; 

cosmic rays 

solar flares 

particle reactions 


Radiation levels in an airplane 

Do solar flares and galactic radia- 
tion present a real danger to people 
in high-altitude jets? When an air- 
plane takes off and begins its as- 
cent, why does the net radiation 
level it experiences decrease for 
the first 1500 feet and then begin 
to increase with altitude? If there 
are significant variations in the 
extraterrestrial radiation, what 
cause those variations? 

1296, pp. 392-393; 1436; 1437. 

ionization and excitation 

Cerenkov radiation 


Flashes seen by astronauts 

Astronauts on the lunar missions 
saw white, starlike flashes when 
they were in space. The flashes 
occurred about once or twice a 
minute and were seen with eyes 
both open and closed. Apparently 
cosmic rays caused the flashes but 
how? Why did the astronauts see 
point flashes (sometimes with 
fuzzy tails) rather than a glow over 
the whole field of vision? Can a 
passenger in a high altitude jet see 
the flashes? (Figure 7.15.) 

1438 through 1451. 

172 The flying circus of physics 


cocM,VtKes,oucM ... 




AM, <9ucH , c?w, oooo, ^eee . . . 

" -p 

Figure 7.15 

(By permission of John Hart 

Field Enterprises.) 

X ray, UV and IR 
interaction with matter 


X rays in the art museum 

Ultraviolet light, infrared light, and 
X rays are often used to find oil 
paintings over which second paint- 
ings have been made. A painter's 
modifications to a picture can thus 
be traced, and lost paintings may be 
found. The technique has also been 
used to expose forgeries. For ex- 
ample, the famous art forger Hans 
van Meegeren would paint his imita- 
tion over an old but worthless paint- 
ing so that the old canvas would 

lend authenticity to the counter- 
feit. X-ray analysis revealed van 
Meegeren as a fraud. 

If ultraviolet and infrared light 
and X-rays will interact with the 
bottom painting, surely they 
must also interact with the top 
one. How, then, are the two 
paintings distinguished? 

/ 10, pp. 190- 193; 1452 through 


Nuclear-blast fireball 

What exactly causes the fireball, 
that brilliant ball of light, in a 
nuclear blast? That is, what 
produces the light? How long does 
the fireball last, and what causes its 
decay? Finally, why is it initially 
red or reddish-brown and later 

219, pp. 306-309; 371, pp. 20 ff; 


Defensive shields in Dune 

In Dune (1460), a classic science 
fiction novel by Frank Herbert, 
people wear personal shields that 
set up some type of "force field" 
that will only pass slowly moving 
objects. Hence, the shield would 
protect you from bullets and knife 
attacks but still allow you fresh air 
to breathe. Is such a protective 
shield physically possible? 

Explaining material 
science to my 

(7.19 through 7.24) 



Can you explain friction to my 
grandmother? I don't mean with 
any really sophisticated ideas, but 
with some simple model. Is it 
caused by surface irregularities 
that jam and mesh together? Or is 
it due to electrostatic forces? Do 
molecular forces bring about 
local adhesion? Or does the harder 
surface penetrate the softer one, 
causing them to stick? This sub- 
ject is so old, so commonplace, and 
so thoroughly investigated that 
surely there is a simple explanation. 

3; 1462 through 1465. 


The flowing roof 

The National Cathedral in Washing- 
ton, B.C., was built to imitate the 
cathedrals of medieval England. 
The roof was made of lead because 
England, with her abundance of 
lead, had put lead roofs on her 
cathedrals. Unfortunately, when 
the roof on the National Cathedral 
was only a few years old, it was 
discovered that "the beautiful, 
delicately colored, lead roof was 
slipping inexorably downward, 
sliding past the nails and battens" 
(1461). Apparently this was due 
to two factors: the latitude of 

The walrus has his last say and leaves us assorted goodies 1 73 

Washington and the high purity 
of modern lead. How do these 
factors explain the slipping of the 




Diamond cutting is the art of 
fracturing a crystal in precisely the 
right way. Sculpture also requires 
good control over fracturing. If 
you have ever cut glass tubing, 
you have probably used the trick 
of first putting a small scratch on 
one side and then snapping the 
tube. This procedure avoids a 
jagged edge. 

What determines where a crack 
will go? Why does one start and 
propagate at all? I can fracture 
a piece of glass with a stress that is 
much less than that needed to 
break the atomic bonding, but 
the bonding is nevertheless 
broken. How is the atom-atom 
ripping accomplished with such 
relatively small applied forces? 

1466 through 1474. 


Chrome corrosion 

Your car's chrome finish may cor- 
rode with time, although recently 
that problem has become much 
less likely. Corrosion would set 
in at the defects in the outer 
layer of chromium (Figure 7.22), 
so in the past car engineers did 
their best to make a continuous, 
thick chromium layer to reduce 


Figure 7.22 

Chrome corrosion develops at 

the defects in the chromium. 

the possibility of such defects. 
However, blemishes were still 
bound to occur through normal 
car usage. Then it was noticed 
that corrosion became much 
less likely if the chrome finish 
were full of many small defects. 
So now small defects are put in 
on purpose. Why does a defect 
in the chromium layer lead to 
corrosion, and why do more 
defects lead to less corrosion? 




Laborious polishing, say of silver 
utensils, is the curse of many a 
person. What does the rubbing 
do? Does it cause fine scale 
abrasion of the surface, melt 
the surface, or smear the hills 
into the valleys on the surface? 
Actually, "the nature of the polish- 
ing process has been an unsettled 
question ever since Isaac Newton 
attempted to explain the physics 
of the process three centuries 
ago" (1477),* although recent 
work has shed more light on it. 
What is meant by a "smooth 
surface"? Smooth compared 
to what? What happens to the 

surface, on the molecular level, 
if the polishing is either abra- 
sion, melting, or smearing? 

1476; 1477. 

*From "Polishing," by E. Rabinowicz. 
Copyright © 1968 by Scientific 
American, Inc. All rights reserved. 


Sticky fingers 

How do adhesives stick? That's 
a simple question to ask but a very 
difficult one to answer. You may 
be tempted to dismiss it by mum- 
bling something about intermolec- 
ular forces, but don't, for there 
are inherent difficulties in such a 
quick answer. 

For example, what holds my cof- 
fee cup together? Intermolecular 
forces? Suppose I crack it in two 
and then carefully piece it back 
together. I'll do such a good job 
that the crack will hardly be 
visible. Will the two pieces stay 
together? Aren't the intermolec- 
ular forces involved the same? 

Glue, paste, or some other 
adhesive would help here, but 
exactly how? Does the adhesive 
have to be sticky? Does it have 
to be fluid? Why will some 
adhesives work in this case where- 
as others will not? Are there 
some materials that cannot be 
made to adhere with any ad- 

There are cases in which one 
really should worry about two 
materials spontaneously adhering 
without an adhesive. In the early 
days of manned space exploration 
there was a real concern that an 
astronaut's metal-soled boots 

1 74 The flying circus of physics 

would spontaneously stick to the 
metal space capsule. What prompt- 
ed the concern? We should be 
thankful such ready adhesion 
isn't common, for otherwise 
the world would have long ago 
ground itself down into a sticky 

950; 1432; 1478 through 1480. 

The walrus has his last say and leaves us assorted goodies 1 75 


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7 Crane, H. R., "Problems for 
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8 Sutton, R. M., "An Introvert 
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17 Reid, W. P., "Weight of an 
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18 Mellen,W. R., "Superball Re- 
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19 Class of W. G. Harter, "Velocity 
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20 Kerwin, J. D., "Velocity, Mo- 
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21 Evans, G., "The Prodigious 
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22 Fox, G. T., "On the Physics 

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30 Bothamley, F. H., "Vehicle 
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31 Garwin, R. L., "Kinematics of 
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33 Byers, C, Cowboy Roping 
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in Searchlight Beam," Am. J. 
Phys., 43, 453(1975). 

1632 Walker, J. D. # "Karate 
Strikes," Am. J. Phys., 43, 845 

Bibliography 217 


Absorption, acoustical, 1.15 

Athletics, see Sports 

Bell, 2.63 

radiation, 3.38, 3.71, 3.75, 

Atomic bombs, 3.24, 3.27, 3.97, 

Belt of Venus, 5.62 



Bernoulli effect. 1.54, 3.34, 

3.95, 6.5 

Atmospheric physics, 1.28, 1.29, 


Acceleration, 2.21 

1.35, 1.36,1.38,1.73-1.76, 

Bicycle, 2.26, 2.29, 2.31,3.16, 

Acoustics, 1.26, 1.27 

3.83, 3.97, 4.68, 4.73, 4.85, 


Adhesion, 7.24 


Big Bertha, 2.52 

Adiabatic process, 3.16, 3.18— 

5.50, 5.58-5.65, 5.99, 

Billiards, 2.27 

3.23, 3.32, 3.46, 3.47, 4.76 


Binaural hearing, 1.70, 1.72 

Airfoil, 2.55, 4.31,4.94 


Bioelectricity, 6.2 

Airplane, 1.24, 1.73,3.1,4.31, 

Aurora, 1.75,6.30 

Birds, 1.37,4.77,4.97,4.98, 

4.32, 4.37, 4.94, 6.27, 6.42, 

Avalanche, 1.6, 3.47 



Bishop's ring, 5.82 

Air tube, 4.2 

Ball lightning, 5.107,6.35 

Blackbody radiation, 3.73,5.106 

Altitude, 2.8, 3.1,3.2, 7.14 

Balloon, 3.5, 7.12 

Blacklight, 5.113 

Aluminum foil, 3.71 

Banjo, 1.8 

Bleaching, 5.103 

Andes glow, 6.48 

Barometer, 3.3 

Blood pressure, 4.3 

Angle of contact, 3.102 

Baseball, 2.2, 2.4, 2.9, 2.12, 

Blow-holes, 3.8 

Angular momentum, 2.40, 2.41, 


Blue arcs, retinal, 5.120 


Bathroom physics, 1.46, 1.48, 

Blue moon, 5.84 

2.69-2.73, 4.54, 4.67 


Blue Ridge Mountains, 5.86 

Antenna, 6.28 


Blue sky, 5.59, 5.61 

Anticorona, 5.79 


Boat, 3.77, 4.7, 4.33, 4.44,4.46, 

Antifreeze, 3.51 

Bathtub, 3.78, 4.67, 4.73, 5.3, 


Antinode, 1.2, 1.44 


Boiling water, 1.12, 3.61, 3.62 

Antiroll tank, 2.60 

Bats, 1.66,2.4,2.13,2.66 

Bolt from the blue, 6.34 

Aquaplaning, 4.44, 4.120 

Bay of Fundy, 4.57 

Book, 2.33, 2.50 

Archery, 2.67 

Beachball, 4.20 

Boomerang, 2.55 

Archimedes's death ray, 3.76 

Beach physics, 1.5, 1.37, 1.42, 

Bores, 4.56 

Archimedes's principle, 4.7, 4.9, 


Bottles, 1.48, 1.57,2.44 



Bowing, 1.7, 1.10 

Arcs, 5.46, 5.120 

Bead lightning, 6.34 

Boyle's law, 3.6 

Art forgeries, 7.16 

Beer's law, 2.53 

Brakes, 2.19 

Artillery, 1.29, 1.65, 1.69, 1.76, 

Bees, 5.55 

Brewster's angle, 5.19 


Beetle, 2.15,4.45 j 



Brocken bow # 5.79 

Bromides, 1.36 

Brownian motion, 1.67 

Bubbles, 3.44, 3.108, 3.109, 
nucleation, 1.13, 1.46, 1.48, 

vibration, 1.12, 1.13 

Buckling, 3.106 

Bullet, 2.49 

Buoyancy, 3.15, 3.23-3.25, 
3.28, 3.29, 3.32, 3.34-3.37, 

Butterfly, 5.94 

Cake, 3.2 

Camera, 5.24 

Candle, 3.110 

Capillarity, 3.38, 3.100-3.107, 

Capillary waves, 4.45 

Carburetor, 3.53 

Cars, 1.1,1.65,2.3,2.5,2.19- 
4.30, 4.79, 4.90, 4.120, 5.48, 

Cats, 2.45, 5.30 
Caves, 3.8 

Cavitation, 1.46, 1.48, 4.105 

Cellophane, 5.52 

Celts, 2.72 

Center of mass motion, 2.7, 2.8, 

Cerenkov radiation, 7.15 
Chair, 2.14 
Chalk, 1.1 

Champagne, 3.6, 3.19 
Cheerios, 3.100 
Cheerleading horn, 1.63 
Chimney, 2.51,3.34 
Chinook, 3.18 
Chlandi figures, 1.7 

Chocolate syrup, 4.125 

Christmas ball, 5.141 

Christmas tree lights, 5.63 

Cigarette, 3.36, 5.89 

Click beetle, 2.15 

Clothes, 1.16,3.79,5.22,6.44 

Cloud maps, 5.72 

Clouds, 3.23-3.29, 3.32, 4.100, 

Coffee, 1.22,3.91,4.70,4.101 
Coherent light, 5.115 
Coin, 4.78, 5.4 
Coke, 1.13, 3.19 
Collisions, 2.10-2.13, 2.16 
Color, 3.92, 5.126, 5.128- 

Combination tones, 1.64 
Combustion, 3.111,3.112 
Condensation, 3.17, 3.22- 

Conduction, acoustical, 1.20, 

thermal, 3.42, 3.45, 3.48, 

3.49,.3.59, 3.69, 3.78, 


Confessional acoustics, 1.27 
Contrail, 3.32 
Convection, 3.44, 3.56, 3.59, 

3.66, 3.70, 3.79, 3.84- 


Convertible, 3.20 
Cooking, 1.12,2.17,3.2,3.515, 


3.80, 6.5, 7.9 
Cooling rate, 3.40, 3.52 
Corn, 7.13 

Corona, 5.80, 5.81, 5.83 
Corrosion, 7.22 
Corrugated pipe, 1.54 
Corrugated road, 2.59 
Cosmic rays, 7.14 
Cosmology, 7.3 
Cracks. 3.113. 3.114. 7.21 

Crapper, 4.107 
Creep, 4.119 
Cross section, 2.1 
Crown flash, 5.47 
Crumbs, 6.17 
Crustacean, 5.111 
Crystals, 3.98, 5.93 
Crystal radio, 6.26 
Cultivation, 3.101 
Current, electric, 5.121, 6.1, 

Current, ocean, 4.61, 4.62, 6.4 
Cusps, 4.60 
Cyrano de Bergerac, 7.2 

Dam, 2.40, 4.1 

Davy mine lamp, 3.1 12 

Death, 2.5, 3.7,4.14, 

Death Valley, 3.21 

Decompression, 3.9 

Desert, 4.102 

Dew, 5.26, 5.41 

Dewbow, 5.41 

Diabolo, 2.70 

Dichroic crystal, 5.56 

Die swell, 4.127 

Differential, 2.41 

Diffraction, acoustical, 1.37, 
1.40, 1.42,1.43 
optical, 5.95-5.98, 5.105 

Diffusion, 3.92, 4.16, 4.131 

Dike, 4.1 

Dilatancy, 4.127 

Discharge, 5.86, 6.32-6.49 

Dispersion, optical, 5.13, 5.16, 
5.32-5.34, 5.58-5.63, 
radio, 6.31 

Distrail, 3.32 

Diving, 3.7, 3.9 

Divining, 7.5 

Doppler effect, 1.65, 1.66 

Drafting, 4.79 

Dragster, 1.1,2.21,4.90 

Drop, 3.65, 13, 

220 Index 

Drowning victim, 4.14 
Drum vibration, 1.3 
Dry dock, 4.9 
Dune, 7.18 
Dunking bird, 3.64 
Dust, 3.111 
Dust devil, 4.71 

Earthquake, 1.45, 6.38, 7.8 

Eat, physics you can, 1.2, 1.18, 
1.19, 1.22, 1.56, 1.57,3.2, 
6.12, 7.9 

Echo, 1.30-1.32, 1.34 

Eclipse, 5.25, 5.99 

Edge oscillation, 4.89 

Edge wave, 4.47 

Eel, 6.4 

Egg, 2.71, 4.23, 4.124, 7.9 

Ekman spiral, 4.61 

Elastic fluid, 4.122, 4.123, 4.129 

Electric eel, 6.4 

Electric field, 5.47, 6.4, 6.9, 6.14, 
6.15, 6.32-6.34, 6.36-6.40, 
6.43, 6.45, 6.50 

Electrocution, 6.1, 6.3, 6.47 

Electrostatics, 6.7-6.18 

Entropy, 3.116 

Eskimo roll, 2.35 

Explosions, 1.29,3.111,3.112 

Eye floaters, 5.96 

Falkland Islands, 2.52 
Fata Morgana, 5.8 
Feedback, acoustical, 1.41, 1.56 
Fences, 4.92, 6.10 
Fibrillation, 6.1 
Fiddlestick, 2.34 
Film creep, 4.119 
Films, 4. 109-4. 11 2, 4. 11 4, 

Fire, 3.35, 4.72 

Fireflies, 5.110 

Fireplace, 3.34 

Fire-walking, 3.69 

Fish, 4.12, 4.82, 4.111, 5.1, 5.5 

Fixed-point theorem, 7.7 

Flachenblitz, 5.47 

Flags, 4.29 

Floaters in eye, 5.96 

Flux, 2.1,3.81 

Fluorescence, 5.113, 5.114,5.131 

Flying, 4.31, 4.32, 4.35, 4.77, 

4.97, 4.98 
FM radio, 6.25 
Focusing, acoustical, 1.27 
Fog, 3.19, 3.30, 5.85 
Fogbows, 5.44 
Foghorn, 1.42 
Fork, 5.95 
Freezing, 3.1 1, 3.39, 3.40, 3.42, 

Friction, 2.19-2.22, 2.79, 4.54, 

and sound, 1.1, 1.2 
Frisbee, 4.34 
Frost flowers, 5.51 
Fundy, Bay of, 4.57 

Galvani, 6.2 
Gegenschein, 5.76 
Gelatin, 4.124, 4.126 
Geysers, 3.66 
Ghosting, 5.6 
Ghost mirage, 5.14 
Ghost wakes, 4.75 
Glare, 5.49 

Glasses, 5.49, 5.112, 5.117 
Glory, 5.79 
Glue, 7.24 
Goggles, 5.1, 5.65 
Golf, 2.6, 4.36, 4.96 
Gramophone, 1.60, 1.64 
Gravitation, 2.74-2.79, 7.1 
Gravity waves, 4.15, 7.4 
Green flash, 5.16 

Greenhouse, 3.83 
Gulf Stream, 4.62 
Gyroscopic motion, 2.69—2.73 

Haidinger's brush, 5.57 
Halo, 5.43, 5.46 
Hammers, 2.11 
Harp, 1.8 
Haze, 5.78, 5.86 
Heat island, 3.93 

pipe, 3.59, 3.64 

stroke, 3.90 
Heiligenschein, 5.26 
Helium, 1.21 
Honey, 4.125 
Horns, 1.60, 1.63 
Hourglass, 2.16,4.6 
Hula-Hoop, 2.30 
Humidity, 3.3, 3.90 
Humming, 5.116 
Hydraulic jump, 4.58 
Hydroplaning, 4.44, 4.120 

Ice, 1.19, 2.25, 2.37, 3.38, 3.43, 


5.43, 5.45 
Ice blink, 5.72 
Icehouse, 3.58 
Ice skating, 2.54 
Impedance matching, acoustical, 

Incandescent bulb, 3.72, 6.6 
Incense swinging, 2.58 
Indians, 1.20 

Induction, magnetic, 6.21-6.23 
Infrared, 7.16 
Infrasound, 1.45 
Insects, 2.15, 3.88, 4.28 
Interference, acoustical, 1.24— 

optical, 5.34, 5.52, 5.59, 5.74, 

water waves, 4.41 , 4.42, 4.44— 

4.47, 4.59 
Invisible man, 5.2 

Index 221 

Ionosphere, 6.30. 

Mach band, 5.127 

Olber's paradox, 7.3 

Magnetism, 6.19-6.24 

Optical activity, 5.54 

Joule heating, 6.1 

Mamma, 3.29 

Orbits, 2.75, 2.76, 2.79 

Judo, 2.48 

Maps, 2.78, 5.72 

Orchard, 3.95 

Jumping, 2.8 

Margarine, 4.126 

Osmotic pressure, 3.103—3.107 

Jumping beans, 2.7 

Masonry wall, 3.107 

Oven, 3.56 

Mayonnaise, 4.126 

Oxbow lake, 4.64 

Karate, 2.10 

Meandering, 4.64 

Kayaking, 2.35 

Mesh, 4.87, 5.105 

Paint, 4.126 

Kelvin-Helmholtz instability, 4.85 

Microwave, 6.5 

Panama Canal, 4.4, 4.5 

Kelvin water dropper, 6.8 

Mie scattering, 5.78-5.90 

Parachute, 4.90 

Ketchup, 4.126 

Milk, 4.70, 4.1 10, 4.1 13, 5.88 

Parhelia, 5.42 

Kinetic gas theory, 3.94 

Mine lamp, 3.112 

Pendulum motion, 2.44, 2.56, 

Kitchen physics, 1.2, 1.12, 1.18, 

Mirage, 5.7-5.11,5.14 


1.19, 1.46, 1.56, 1.57,2.17, 

Mirror, 5.12, 5.15, 5.74 

Pepper, 4.117 


Mock sun, 5.42 

Percolator, 3.67 

3.57, 3.59, 3.62, 3.63, 3.65, 

Moire 7 patterns, 5.142 

Perpetual motion, 6.24 


Moment of inertia, 2.33, 2.37- 

Phosphenes, 5.121 


2.39, 2.42, 2.74 

Phosphorescence, 5.131 


Moon, 2.74, 2.76, 2.77, 4.52- 

Photochemistry, 5.110-5.112 

4.124-4.126, 5.4, 5.54, 5.95, 


Pie pan, 3.75 



Pillars, 5.39, 5.45 

Kites, 4.99, 6.39 

Mountains, 2.78, 3.22, 3.60, 5.7 

Pinhole optics, 5.23-5.25 

Knuckles, 1.17 

Mother-of-pearl clouds, 5.73 

Ping-pong ball, 2.18 

Kundttube, 1.47 

Mud, 3.113, 5.87 

Pipes, 1 .44, 1 .46, 1 .54, 3. 1 1 , 3.70 

Mushroom, 3.24 

Plastic wrap, 5.52, 6.18 

Lake, 4.102, 4.109, 5.67, 5.101 

Music, 1.3, 1.4, 1.8, 1.10, 1.23, 

Plumes, 3.37 

Land color effect, 5.128 


Poisson spot, 5.98 

Lapse rate, 3.37 

Mustard, 4.126 

Polarization, 5.19, 5.36, 5.48-5.57 

Laser, 5.17, 5.104, 5.115 

Pole vaulting, 2.8 

Lasso, 2.32 

Nappe oscillation, 4.89 

Polishing, 7.23 

Latency, visual, 5.117, 5.122 

Nerves, 6.2 

Pond, 3.44 

Latent heat, 3.22, 3.40, 3.43, 3.52, 

Noctilucent clouds, 7.4 

Pool shots, 2.27 

3.54-3.62, 3.64, 3.68, 3.93 

Noise, 1.68 

Porpoise, 4.51 

Lead, 3.69, 7.20 

Non-Newtonian fluids, 4.122— 

Pouring, 1.48,4.118 

Leaves, 4.102, 5.25, 5.28 


Power, 1.62,2.15 

Levitation, 4.21, 4.22, 5.104, 6.21, 

North Sea, 4.1 

Power lines, 6.50 


Nuclear bomb, 3.24, 3.27, 3.97, 

Prairie dog, 4.27 

Lightning, 1.38, 5.47, 6.32-6.48 


Precession, 2.26, 2.69 

bugs, 5.110 

Pressure, barometric, 4.13 

rod, 6.40 

Ocean physics, 3.9, 4.9, 4.10, 

gas bubbles, 4.105 

Liquid crystal, 5.93 

4.12, 4.16, 4.41-4.43, 4.46- 

hydrostatic, 4.12, 4.13, 4.130 

Liquid rope coil, 4.125 


negative, 3.103 

Looming, 5.7 


phase change, 3.46—3.49 

Lowitz arc, 5.46 

Oil, 4.78, 4.1 01, 4.1 08, 4.1 25, 5.91 

Pressure cooker, 2.17 

222 Index 

Projectile motion, 2.2, 2.49, 2.52 

Protein structure, 7.9 

Pump, 3.16 

Purkinje, 5.122, 5.124, 5.126 

Purple light, 5.58, 5.60 

Quicksand, 4.130 

Race cars, 1.1, 1.65, 2.42, 4.30, 

4.79, 4.90 
Radiation, 7.14, 7.15 
Radiation force, 5.104 
Radiator, 3.68, 3.70 
Radio, 1.64, 6.25, 6.26, 6.28,6.29 
Rain, 2.1,5.31,6.43 
Rainbow, 5.32-5.41, 5.44 
Ranque-Hilsch vortex tube, 4.76 
Rayleigh jet, 4.113 
Rayleigh scattering, 1.30, 5.58, 5i59 
Rayleigh-Taylor instability, 4.15, 

Rayleigh waves, 1.31, 1.34, 7.8 
Rays of Buddha, 5.135 
Records, 1.4 
Reflection, acoustical, 1.27, 1.30, 

1.31, 1.74 
optical, 5.2 f 5.6, 5.12, 5.15, 5.17, 


Refraction, acoustical, 1.28, 1.29, 

1.33, 1.35, 1.38, 1.39, 1.73 
optical, 5.1,5.3-5.11,5.13, 



water waves, 4.48 
Refrigerator, 3.74 
Resonance, acoustical, 1.1. 1.2, 

oscillations, 2.56-2.68 
water waves, 4.55, 4.57 
Rice Krispies, 1.18 
Rivers, 2.53, 4.64 
Rockets, 1.69 
Rocks, 2.40, 3.105, 4.7 
Rope coil, liquid, 4.125 

Rope tricks, 2.32 

Rotating frame, forces in, 2.52— 

Rubber band, 1.11,3.13 
Rubdown, 3.52 

Sailing, 4.33 

Saint Elmo's fire, 6.46 

Salt ring, 3.63 

Salt water, 4.4, 4.5, 4.16-4.18 

Sand castles, 6.17 

dunes, 1.6,4.102,4.106 

footprints, 7.11 

ripples, 4.104 

vibrations, 1.5, 1.6, 1.7 
Santa Ana, 3.18 
Sap, 3.103 
Satellites, 2.75 
Schooling, 4.82 
Scotch tape, 6.11, 7.10 
Screen, 5.105 
Scuba diving, 3.7 
Seagulls, 1.37 
Searchlights, 5.75, 5.137 
Seashells, 1.49 
Seasons, 3.81 

Secondary flow, 4.63, 4.64 
Seiches, 4.55 
Shadow, 1.76, 5.23, 5.25, 5.87, 

Shadow bands, 5.99, 5.100 
Shampoo, 4.123 
Shark, 4.51 
Shaving cream, 4.126 
Shearing, 1.5, 1.6,4.126,7.11 
Ship, 2.60, 4.9, 4.37, 4.46 
Shockwaves, 1.73, 1.74, 1.76, 

4.56, 4.58 
Shower, 1.51 
Shrimp, 3.89 
Signal-to-noise ratio, 1 .68 
Silent zones, 1.29 
Silicone putty, 4.127, 4.128 
Singing, 1.51, 1.52 
Sink physics, 1.46, 1.48, 3.10, 

4.47, 4.58, 4.59, 4.67, 4.87, 

Siphon, 4.105, 4.107, 4.129 
Skating, 3.46 
Skid, 2.37 
Skiing, 2.46, 2.59, 3.45, 4.95,5.65 
Skipping rock, 2.40 
Sky brightness, 5.64, 5.66 
color, 5.58-5.62, 5.68 
polarization, 5.50, 5.55—5.57 
Smoke, 3.35-3.37, 4.103, 5.89, 

Snow, 1.14, 1.15,3.45,3.48- 

3.50, 3.96, 3.99, 4.92, 4.93, 

avalanche, 3.47 
blindness, 5.139 
wave, 7.6 
Soap, 4.1 17, 5.91,5.113 
Soaring, 4.98 
Solar flares, 7.14 
Sol-gel change, 4.126 
Sonar, 1.39, 1.66 
Sonic booms, 1.73, 1.74 
Soup, 4.122 
Space, 3.82, 3.84 
Speakers, 1.60, 1.62, 1.64 
Speckle pattern, 5.115 
Speed of sound, 1.21-1.23, 1.28, 

Speedometer, 6.23 
Spillway, 4.89 

Splashing, 1.13, 4.88, 4.1 13, 6.14 
Spoon, 4.24 
Sports, 2.2, 2.4, 2.6, 2.8-2.10, 


2.66, 2.67, 3.45, 3.46, 4.33, 

4.36, 4.39, 4.40, 4.50, 4.88, 

4.95, 4.96 
Spray gun, 4.25 
St. Elmo's fire, 6.46 
Stacks, 1.37 
Stars, 5.66, 5.97, 5.102, 5.106, 

Steam devil, 4.73 
Stewardess, 3.1 

Index 223 

Stones, 2.40, 2.72, 3.105, 3.115 

Toilet paper, 2.39 

Watches, 2.64,3.14 

Streetlights, 5.63, 5.122 

Toilets, 4.107 

Water bug, 4.45 

Stress, 1.14,4.124, 5.93, 7.11-7.13 

Tomato soup, 4.122 

bell, 4.1 14 

String telephone, 1.9 

Tops, 2.69, 2.73, 5.118 

Waterfall, 2.65 

vibrations, 1.8—1.11 

Tornado, 1.33, 1.45, 4.68, 4.69, 

Water glass, 4.13, 4.15 

Stroboscope, 5.116, 5.118, 5.131 


hose, 4.8 

Subjective tones, 1.64 

Torque, 2.23, 2.24, 2.31, 2.35, 

pipes, 1.46,3.11 

Submarine, 1.39, 3.7, 4.10 

2.39-2.41, 2.44-2.46, 2.49- 

sheet, 4.115 

Sugar, 4.78, 5.108, 6.12 


spout, 4.68 

Sunburn, 5.109 

Toys, 1.9, 1.54, 1.58,1.61,2.7, 

stream, 4.19, 4.22, 4.24, 4.114- 

Sun dog, 5.42 



Sunglasses, 5.49, 5.112, 5.117 

2.47, 2.68-2.70, 2.72, 2.73, 

witching, 7.5 

Sun pillar, 5.45 


Waveguides, acoustical, 1.25 

Sunsets,5.16, 5.58, 5.60-5.62, 5.100 


Wave speed, 4.43, 4.56 

Suntan, 5.109 

Trains, 2.26, 2.59, 4.26 

Waves, water, 4.41-4.60, 4.1 15 

Superball, 2.18, 2.28 

Triangle, luminous, 5.21 

Weight, 2.16 

Supercooling, 3.39 

Triboelectricity, 6.7, 6.10, 6.12 

Weissenburg effect, 4.124 

Supernumerary, 5.34 

Triboluminescence, 5.108 

Wells, 3.4 

Surface tension, 3.5, 3.102, 3.108, 

Tunnel, 3.6 

Wetting, 3.100, 3.102 


Turbulence, 1.33, 4.85-4.88, 

Whip crack, 1.77 


5.99, 5.102 

Whirligig beetle, 4.45 

Surface wave, 1.31, 1.34, 7.8 

Whiskey, 4.1 19 

Surfing, 4.49-4.51 

UFO's, 7.1 

Whispering, 1.43, 1.50 

Syrup, 4.125, 5.54 

Ultrasound, 1.66 

gallery, 1.31 

Swimming, 4.88, 5.1, 5.92 

Ultraviolet light, 5.103, 7.16 

Whistlers, 1.25 

Swinging, 2.56, 2.58 

Unicycle, 2.61 

Whistling, 1.56-1.59, 1.61 

U-tube, 3.15 

wires, 1.55 

Tacoma Narrows Bridge, 4.84 

Wien's law, 3.97 

Tailgating, 4.79 

V-2 rockets, 1.69 

Wind, 1.35, 1.53, 1.55, 3.18, 3.86, 

Taylor's ink walls, 4.66 

Vee formation, 4.77 

4.33, 4.38, 4.83-4.85 

Tea leaves, 4.63 

Ventilator, 4.27 

Windchill factor, 3.52 

Teapot, 1.56 

Venus, Belt of, 5.62 

Window, 5.6 

Television, 5.116, 5.118, 5.132, 

Vibration and sound, 1.1-1.11 

Windshield, 4.28, 5.53, 5.77 

6.25, 6.27 

Vikings, 5.56 

Wineglass, 1.2 

Temperature of space, 3.82, 3.84 

Violin, 1.10 

Wings, 4.30, 4.31. 4.35, 4.37,4.94, 

Thermal expansion, 3.110—3.115 

Viscosity, 4.124-4.126, 4.130 


Thermometer, 3.12 

Vision, 5.115-5.141 

Wire mesh, 4.87, 5.142 

Thixotropic fluids, 4.126 

Visual latency, 5.117, 5.122 

Work, 2.21 

Three-dimensional perception. 

Volcano, 5.82, 6.37 


Vortices, 1.47, 1.57, 1.61, 4.67- 

X-rays, 5.127,7.16 

Thunder, 1.38, 1.74 
Thunderstorm, 3.41, 3.86 
Tides, 4.52-4.57 

4.85, 4.90, 4.92, 4.94, 4.98, 

Yoyo, 2.47 
Yubana, 3.61 

Tight-rope walking, 2.43 

Wakes, 4.44-4.46, 4.75, 4.77- 

Zenith blue, 5.61 

Ti res. 220. 2.36. 2.38. 3.49. 4. 1 20 


Zodiacal light, 5.76 

224 Index 

Short Answers 

There are several very real 
dangers in writing answers, even 
short ones, to The Hying Circus. 
First of all, my references and my 
physics may be wrong. This 
danger may especially be true with 
those questions dealing with topics 
still under research, such as ball 
lightning, whose nature is 
sometimes tackled in every other 
issue of some of the journals. AH I 
can say about my answers here is 
that they are the best I can do in a 
very small amount of space and 
with the currently available 
literature. Please remember that 
these short answers are but the tip 
of the iceberg; there is much 
physics below each. And you 
should not take them as the last 
word; instead, you should take 
them as starting points and then 
update them as new papers and 
articles appear. 

The second danger in writing 
answers is more serious and 
makes me hesitate in even trying. 
You may flip to the answer section 
of this book so quickly that you 
miss the excitement of the 
question. Unless you savor the 
questions, even to the point of 
some frustration, you will miss the 
point of this book. The potential for 
learning how to examine the world 
in which you live lies much more in 
the first part of this book than in the 
second. So, please spend as much 
time as you can worrying over your 
own answers before you turn to 
this section or search the library for 

1.1 The squeal heard in these 
several situations results from 
"stick and slip." For example, the 

incorrectly held chalk first sticks on 
the chalkboard, but when the writer 
bends the chalk sufficiently, it 
suddenly slips and then vibrates, 
periodically striking the chalkboard 
and producing the squeal we hear. 
As the vibrations decrease, the 
friction between the chalk and the 
board increases until the chalk 
sticks once again. 

1 .2 The finger excites the 
longitudinal oscillations, that is, the 
vibrations along the perimeter of 
the rim. The rim also oscillates 
transversely, that is, perpendicular 
to the rim. This second type of 
oscillation causes the fluid motion 
since it is a motion into and out of 
the liquid. The antinodes of the 
transverse oscillations and hence 
of the fluid motion are 45° from the 
antinodes of the longitudinal 
oscillations. Since the finger's 
position must be a place of 
maximum longitudinal motion and 
thus a longitudinal antinode, the 
fluid motion must have an antinode 
45 c behind the finger. 

1.3 Imagine that one membrane 
is oscillating and the other is not. 
The moving membrane begins to 
excite the other by pushing on the 
air between them. As the second 
membrane begins to oscillate, 
however, the air thereafter hinders 
the oscillations of the first 
membrane, eventually stopping it. 
By the time the air has maximized 
the oscillations of the second 
membrane and stopped the first, 
the situation is reversed, and the 
air then transfers the oscillation 
back to the first membrane. 

1.4 To press the bass into the 
records at the same intensity level 
as the higher frequencies would 
require an oscillation of the needle 
that would carry it into the adjacent 


1.5 and 1.6 In both of these 

cases the sound apparently results 
from the oscillation of the sand 
when parts of it are forced to move 
under a shearing stress. In the 
footstep the sand beneath the foot 
is forced downward; in the sand 
dune a small avalanche causes 
some sand to slide over another 
part. Although the noise production 
is not understood, it is apparently 
confined to sand having mostly 
spherical grains of uniform size. 

1 .7 The drawing of the bowstring 
on the edge of the plate sets the 
plate into vibrations. The pattern of 
the vibration, that is, where there 
are the maximum and minimum 
amplitudes, depends on the shape 
of the plate and where it is forced 
to have no vibrations because it is 
held in place. During the bowing, 
the sand, initially in the areas of 
maximum vibration (called 
antinodes), is thrown to the areas 
of no vibration (called nodes), 
eventually collecting in order to 
indicate the vibrational pattern. 
The fine dust would do the same 
except that it is carried by the air 
currents set in motion by the 
vibration. Since these currents 
blow across the plate from the 
nodes to the antinodes and then 
upward, the dust is carried to the 
antinodes and deposited. 

1 .8 More of the higher frequency 
harmonics are excited when the 
banjo is plucked with the fingernail 
or with a sharp pick than when the 
string is pulled with a finger. These 
higher frequencies give a twangy 
quality to the banjo's music. 

1.9 The voice vibrates the can, 
which then excites waves on the 
string. These waves excite the 
second can in a reverse way to be 

Answers 225 

heard. The can does not respond 
to the lower frequencies in your 
talk, and thus those frequencies 
will be missing at the other end, 

making your words thin. 

1.10 The bow alternately sticks 
to the strings and then slips, 
leaving the strings oscillating 
during the intermediate time of 

1.11 The f requ ency of a vibrating 

string depends on the string's 
density, length, and tension. If a 
string is tightened, the first two 
remain constant, and the 
increased tension raises the 
frequency of vibration. If a rubber 
band is stretched, however, all 
three of the quantities change so 
that the frequency is essentially 

1.12 The first sound comes when 
the bottom of the pan is heated and 
small bubbles form, each with a 
click and collectively with a hiss. 
With further heating, the bubbles 
detach from the bottom, rise into 
the cooler water, and then 
collapse, creating a louder noise. 
This noise continues until the water 
is sufficiently hot for the bubbles to 
reach the surface to break. Then 
the water is in full boil, and the 
noise of the bubbles reaching the 
surface is a softer, splashing 

1.13 Part of the sound of the 
brook is due to the bubbles formed 
in the running water. The creation 
of a bubble has little sound, but the 
volume oscillations and the 
collapse of a bubble produce much 
more sound. 

1.14 If the ground is very cold 
(-10T or lower), the ice beneath 
your feet cannot melt due to your 
weight and will snap instead. (Also 

see FC 3.46-3.49*.) 

1.15 The small spaces in the 

snow's surface absorb the sound 
just as acoustic tile does in most 
modern offices. As the snow 
becomes more packed, this sound 
absorption is reduced. 

1.16 Any periodic motion can 
produce sound waves. The 
periodic jerking as the individual 
threads snap when you rip cloth 
will set up sound waves for you to 
hear the ripping. 

1.17 The popping is due to the 
bursting of tiny gas bubbles in the 
fluid lubricating the finger joints 
when the fingers are pulled and the 
fluid pressure is thereby reduced. 
Several minutes are needed 
before the gas is reabsorbed and 
ready for an encore. 

1 .18 The sound is caused by the 

release of air from the cereal 
grains as those grains become 
soggy in the milk and eventually 

1.19 The cracking is due to the 
thermal stresses in the ice as the 
ice warms. The "frying" sound, 
however, is due to the bursting of 
tiny air bubbles trapped in the ice 
as the surface reaches those 
bubbles. Ice free of such bubbles 
will melt with only the cracking. 

1.20 The fact that the speed of 

sound is greater in ground than in 
air is not important since horses 
travel much slower than sound. 
The main advantage in listening to 
the ground is that there are less 
objects in the sound's path to 
scatter and attenuate the sound. 

1 .21 The resonant frequencies of 

* These citations refer to the answers 
in this book. 

your mouth (as any other 
resonating volume of gas) depend 
directly on the speed of sound in 
the gas in it. The speed of sound is 
greater in helium than in air, and 
therefore your voice will have a 
higher pitch. 

1 .22 Air trapped on the powder is 
released as the powder dissolves. 
Since the speed of sound is lower 
in air than in water, the speed of 
sound in the air- water mixture is 
lower than in pure water. During 
that period while the air escapes 
the container, the resonant 
frequencies of the water, which 
depend directly on the speed of 
sound, will also be lower. Hence, 
you hear a lower tone until the air 

1.23 Because resonant 
frequencies in a wind instrument 
depend directly on the speed of 
sound, those frequencies increase 
as the player warms the instrument 
with his or her breath and thereby 
increases the speed of sound in it. 
Warming of the string instruments 
by friction will expand the string, 
thus decreasing the tension on the 
strings, which decreases the 
resonant frequencies of the string 

1.24 Within a couple of meters 
from the ground, the sound directly 
from the airplane can interfere with 
the sound reflected from the 
ground to enhance certain 
frequencies. The height at which 
constructive interference can occur 
(where one sound wave will 
reinforce another) depends on the 
wavelength of the sound. The 
nearer the ground, the shorter the 
wavelength will be for constructive 
interference. So, near the ground 
you will hear more of the short 
wavelengths, and thus high 

226 Flying circus of physics with answers 

frequencies. As you raise your ear 
more, longer wavelengths and thus 
lower frequencies will be heard. 

1 .25 The sound that is reinforced 
in its travel through the culvert 
must reflect from the walls at a 
certain angle, which depends on 
the wavelength of the sound. The 
longer wavelengths that are 
reinforced and eventually heard 
must reflect at a greater angle than 
the shorter wavelengths and 
therefore travel less along the 
culvert's length between each 
reflection and take longer to reach 
the end. A listener at the end will 
thus first hear the shorter 
wavelengths {higher frequencies) 
and then progressively longer 
wavelengths (lower frequencies). 

1 .26 To have a distinct echo, the 
reflected sound must come no 
closer than 50 msec to the direct 
sound. Eliminating reflections from 
the walls will drastically reduce the 
acoustic richness of the room. The 
waits are designed to diffuse the 
sound throughout the room. Some 
of the scatterers on the walls 
should be small to scatter the short 
wavelengths (high frequencies) 
whereas other features should be 
larger to scatter the longer 
wavelengths (lower frequencies). 
The scattering should be diffuse 
enough to eliminate dead spots of 
destructive interference in the 

1.27 Sound rays emitted from 
one focus in an elliptical room will 
cross at the other focus, thus 
making a conversation at the first 
focus audible at the second. 

1 .28 Sound travels faster in 
warmer air than cooler. If the air 
temperature decreases upward, 
the top portion of an initially 

horizontally traveling sound wave 
will propagate slower than the 
lower part, and the wave path will 
bend upward. With such a normal 
temperature distribution, the sound 
will not be able to travel very far 
along the ground before this 
refraction has bent it away from the 
ground. On a cold day the air 
temperature may increase upward, 
especially just over a body of 
water, thus refracting the sound 
downward instead of upward. 
Hence the sound will be kept near 
the ground longer. 

1.29 The speed of sound in air 
increases as the air temperature 
increases. Thus, as a sound wave 
reaches the increasingly warmer 
air in the stratosphere, the higher 
portion of the wave will travel faster 
than the lower portion, causing the 
wave path to bend over and 
eventually turn downward. Sound 
will be heard where it reaches the 
ground. In the meantime, some 
direct sound from the source will 
travel horizontally until it is 
scattered or absorbed by the 
objects on the ground. Between 
the outer region of this horizontal 
propagation and the region where 
sound is returned from the 
stratosphere, there is a region in 
which sound from the source is not 
heard. If the sound returned from 
the stratosphere is reflected by the 
ground sufficiently well that it can 
return to the stratosphere, it can be 
bent over and returned to the 
ground once again to give yet 
another region of sound, the outer 
white area in Figure 1.29. 

1.30 The scattering of sound by 
objects small with respect to the 
wavelength of the sound will 
depend inversely on the fourth 
power of the wavelength. The 

shorter wavelengths (higher 
frequencies) will therefore be 
scattered more than the longer 
wavelengths (lower frequencies). 
An echo of a yell will thus be higher 
pitched because the higher 
frequencies are more strongly 

1.31 In continuously reflecting 

from the walls of the dome, the 
sound waves are reinforced in a 
narrow belt around the perimeter of 
the wall. If the listener stands 
inside this belt, he or she can hear 
the whisper. Further from the wall, 
however, the reinforcement 
decreases and the whisper 
becomes inaudible. A whisper 
works better because it has more 
of the high frequency sounds than 
does normal talking, and the 
audible belt is wider with higher 

1.32 Suppose you are facing a 
picket fence. The sound reflected 
from a particular picket on your left, 
say, will return to you slightly 
sooner than the sound reflected 
from the next picket more to your 
left, because that next picket is a 
little further away from you. The 
sound returned first comes from 
the nearer pickets, and then 
progressively later sound returns 
from progressively more distant 
pickets, producing a musical tone 
to the echo. The frequency of the 
tone is the inverse of the time 
interval between reflections from 
adjacent pickets. 

1-33 Sound from outside the 
funnel may not be able to reach the 
inside, because it is refracted so 
strongly by the high velocity winds 
around the funnel. The interior of 
the funnel may also appear to be 
silent, because hearing is difficult if 
one is suddenly thrust into a low 

Answers 227 

pressure region. (Hearing is 
difficult in flying until the ears have 
a chance to adjust to the pressure 
changes in ascending and 

1 .34 There is no one answer to 
this question since, depending on 
the bridge, either effect may 
dominate or both may be equally 

1.35 Sound goes further along 
the ground downwind not because 
there is less attenuation, but 
because the sound waves are 
refracted downward in that 
direction, whereas they are 
refracted upward in the upwind 
direction. Because of the obstacles 
on the ground, the wind velocity 
normally increases with height. An 
initially horizontally traveling wave 
moving downwind will have its 
upper portion moving at a greater 
speed than its lower portion, 
causing the wave to refract 
downward. By similar reasoning, a 
sound wave traveling upwind will 
be refracted upward. 

1 .36 Brontides are most likely 
the anomolor ^ sound propagation 
of FC 1.29, with the unseen and 
distant sources being anything 
from explosions to thunder. 

1.37 Sound waves are diffracted 

by the aperture between the stacks 
and thus sent into the area behind 
the stacks. The angular width of 
the diffraction pattern (the angle 
over which the sound will be 
spread by the aperture) is greater 
for longer wavelengths. Thus, if the 
birds had a lower frequency 
squeal, the sound would spread 

1.38 For reasons similar to those 
in FC 1.28 and 1.29, the sound 
waves from a lightning stroke will 

be refracted upward by the warmer 
air near the ground. Beyond a 
range of about 1 5 miles, the sound 
is refracted so much that it is 
traveling upward and then, of 
course, cannot be heard by a 
ground observer. 

1 .39 This problem involves a 
similar refraction of sound waves 
by a change in temperature with 
height Normally the water 
temperature decreases downward 
with depth. Hence, a sound wave 
issued horizontally will be bent 
over and sent downward because 
its upper portion being in warmer 
water, will travel faster than its 
lower portion, being in cooler 
water, The refraction of the sound 
may be so severe that all the 
sound is bent downward and away 
from the submarine. 

1.40 Sound is diffracted by the 
aperture just as in FC 1.37. 
Although the door may be almost 
closed, the sound coming through 
the remaining opening spreads 
through the room. 

1.41 Sound from the guitar 
player's speaker would be picked 
up by his or her guitar, reamplified, 
and then emitted by the speaker a 
short time later. The frequency of 
the ringing is the inverse of the 
time needed to emit a sound once 
the guitar pickup is activated. 

1 .42 The angular width of the 
diffraction pattern (i.e., the angle 
over which the sound is spread 
when it propagates through the 
opening) is greater the narrower 
the opening is. Hence, the 
narrower width provides more 
spread and should be oriented 
horizontally as shown in the figure. 

1.43 Barring reflection of the 
sound from nearby objects, you 

hear your friend when your friend is 
turned away because the sound 
diffracts around his or her head. 
The angular width of the diffraction 
pattern is larger for smaller 
wavelengths (higher frequencies). 
Since whispering is composed 
largely of high frequencies, it can 
be heard better than normal 
speaking because the whispering 
is diffracted more. 

1.44 The effective length of a 
tube is increased by about one 
third of the tubes diameter for 
each open end. This lengthening 
will increase the wavelengths of 
the tube's harmonics (thus 
decreasing the resonant 
frequencies) and can be noticeable 
in wider tubes. 

1.45 The low frequency sound 
can oscillate your chest, for 
example, because the variations in 
air pressure are sufficiently slow 
that your chest can follow them, 
internal hemorrhage can result 
from organs being forced to rub 
against each other during their 
oscillations. Lower intensity levels 
may just cause dizziness and 
nausea. Common car sickness 
may partially result from the 
infrasound produced by the car, 

1.46 With increased flow rates 
through the restricted portions of 
the pipes, turbulence can occur, 
leading to cavitation (formation of 
bubbles). Oscillations of the air 
bubbles can be amplified by the 
pipe and the wails, ceilings, and 
floors to which the pipes are 

1.47 The vibrations of the rod 
create a standing sound wave in 
the tube. Powder at the antinodes 
of air motion in the tube is 
gradually shaken toward the nodes 

228 Flying circus of physics with answers 

where it collects in the larger piles 
shown in the figure. If the air flow is 
sufficiently rapid, vortices are 
created. The smaller ripples of dust 
are formed where two adjacent 
vortices rise or descend together. 

1.48 From the noise of the 

pouring water, those frequencies 
that will resonantly excite the air 
column in the bottle will be picked 
out, enhanced, and heard. Of 
these the loudest frequency will be 
the lowest one, but the value of 
that frequency depends on the 
volume of the air column. The 
greater the volume, the lower the 
frequency. Thus, as water is 
poured from the bottle, the 
resonant frequency that is heard 

1.49 Noises from the 
environment, including the slight 
whispers of a breeze passing the 
shell, will excite the shell's air 
volume at its resonant frequencies. 
The coming and going of these 
resonant frequencies gives the 
listener the illusion of hearing the 
ocean waves come and go. 

1.50 The length and tension of 
the vocal cords determines the 
pitch of the voice. As the air 
pressure in the trachea increases, 
the ccrds are suddenly forced 
apart and then returned to their 
normal position. Continued 
oscillations of the cords produce 
the air pressure variations that 
excite the resonant harmonics of 
the mouth and nasal cavities. 
Usually a man's voice has lower 
pitch than a woman's because a 
man usually has thicker and longer 
vocal cords which will vibrate at 
lower frequencies. A boy's voice 
"breaks" during the rapid growth of 
the larynx, and the vocal cords 
change from being short and thin 

to those of a man. During 
whispering the vocal cords are 
removed from the larynx by relaxing 
them. The frequency of the sound 
will then depend on the oscillations 
created by other obstacles in the air 
stream and on the resonant 
frequencies of the mouth and nasal 

1.51 Were you to sing in a large 
open area, you would hear your 
voice only as it is being produced. 
In the shower stall each sound will 
reflect many times from the close 
walls, prolonging the sensation 
when it is heard, and thus adding 
brilliance (continuation of the high 
frequency sounds) and fullness 
(continuation of the low frequency 
sounds) to your singing. 

1.52 A glass will oscillate at 
certain resonant frequencies. 
Should a singer sing for several 
seconds at one of these 
frequencies, the oscillations of the 
glass can build up to the level 
where the glass cracks. 

1.53 The wind can howl by 
whistiing through wires and bare 
tree limbs (FC 1.55) or by creating 
edge tones (FC 1.56) on roof 
corners or other sharp obstacles, 

1.54 Air flows from the held end 
to the circling end, because the 
rapid motion of the circling end 
reduces the air pressure there, 
whereas the air pressure at the 
held end is atmospheric pressure. 
As the air flows through the tube 
and over the corrugations, if begins 
to oscillate. The frequency of these 
oscillations is determined by the 
spacing of the corrugations and the 
flow speed of the air. From the 
small range of oscillations 
produced with a given twirling 
speed, the tube picks out its own 

resonant frequency to enhance, 
and that is the tone you hear from 
the tube, A faster twirling speed 
moves the range of air oscillations 
into higher frequencies, and a 
higher frequency harmonic of the 
tube is then exicted and heard. 

1 .55 As the wind passes a wire 
or bare tree limb, the air can 
become unstable and shed 
vortices from the obstacle. On a 
telephone wire, for example, 
vortices will be released alternately 
on the top and bottom of the wire. 
These vortices create the pressure 
variations that eventually reach our 
ears to be heard. If the wind is 
strong enough, the pressure 
variations on the two sides of the 
wire can cause the wire to vibrate, 
but that vibration is not necessary 
to the production of the sound. 
Because the pressure variations 
are due to the vortices produced 
on the two sides, the wire is forced 
to vibrate perpendicular to the air 

1.56 In the edge-tone setup, 
vortices are shed from the edge 
when the air stream strikes it. The 
reaction force of the edge then 
creates the sound we hear. Some 
of the sound returns to the source 
of the air stream, causing instability 
in the stream, which creates more 
vortices downstream. When the 
vortices reach the edge, more 
sound is produced, and the whole 
procedure is repeated. In the 
hole-tone production, the sound 
that is returned to the source of the 
air stream changes the speed of 
the air stream and causes vortex 
rings to form (such as in cigar 
smoke rings). When these rings 
strike the hole, more sound is 
produced and, again, the 
procedure is repeated. 

The common tea kettle whistles 

Answers 229 

by hole-tone production. The cap 
on the kettle has two small holes 
spaced with a small cavity. When 
air from inside the kettle passes 
through the first hole, that hole acts 
as the air stream source for the 
second hole. At first the air stream 
is too slow for the necessary 
instability of the air at the second 
hole to cause sound. As the water 
approaches boiling, however, the 
air moves faster so that the 
vortices at the second hole are 
strong enough for the sound to be 

1.57 A coke bottle, a flute, and a 
recorder are different whistles than 
the ones in FC 1 .56 because of the 
addition of a resonant cavity 
adjacent to the edge or hole where 
the instability is produced. From 
the range of frequencies in the 
sound made at the edge or hole, 
the cavity selects its resonant 
frequency to enhance, and that is 
the frequency heard. 

1.58 The air stream blown into 
the police whistle creates an edge 
tone from which the adjacent cavity 
selects its resonant frequency. The 
ball inside the cavity periodically 
blocks the air holes and causes the 
whistling to warble. 

1.59 Normal whistling through 
your lips appears to be a hole tone 
(FC 1,56) with an adjacent 
resonating cavity (the mouth), but 
the details of the air flow do not 
seem to be worked out. 

1.60 The horn and the air 
contained in it provided resistance 
against which the diaphragm could 
work and which would transform 
high velocity motion over a small 
area to low velocity motion over a 
larger area. A long narrow tube 
would store the energy in standing 

waves and select only its resonant 
frequencies. A diaphragm opened 
to the room without a horn would 
be able to move so freely that 
relatively little of its oscillation 
energy would be transferred to air 

1.61 The sound is apparently 
due to pressure variations in the 
unstable vortices emerging from 
the central stem. 

1 .62 There are two main reasons 
for the difference in size. A large 
paper cone cannot respond quickly 
to a high frequency sound, 
breaking up into assorted waves 
over its surface instead. Thus, a 
smaller cone is used for the higher 
frequency range. Second, the 
speaker should spread its sound 
over a wide angle to fill the room. 
The angle of the diffraction pattern 
will depend on the relative size of 
the wavelength and the speaker 
cone. Short wavelengths (high 
frequencies) on a large cone will 
have a small diffraction pattern and 
thus will be beamed into the room. 
Therefore, the short wavelengths 
must come from a small speaker to 
be spread well into the room. 

1.63 Normally the sound directly 
from the mouth diffracts to spread 
nearly uniformly in all directions. A 
cheerleading horn with a large 
front end will have considerably 
less diffraction because the open 
end is larger than the wavelengths 
in the cheerleader's yell. Thus, the 
sound in the direction of the horn 
will be louder than if no horn is 

1.64 The bass notes will be 
produced in the ear even if none 
are issued from the speaker. If two 
different frequencies are incident 
on the ear, its nonlinear response 

produces vibrations having 
frequencies equal to the sum or 

difference of the incident 
frequencies, or the sum or 
difference of some integral multiple 
of those frequencies. The most 
prominent of these extra notes is 
the difference frequency, which 
gives the listener a bass note. 

1.65 The frequency heard by a 
listener depends on the relative 
speeds of the listener and the 
source. Such a shift in the detected 
frequency from the frequency 
issued according to the source is 
called the Doppler shift. As a race 
car approaches a stationary 
listener, the car's whine is Doppler 
shifted up in frequency; as the car 
recedes, its whine is Doppler 
shifted down in frequency. 

1.66 Exactly how a bat extracts 
information from its signal is 
current research and not well 
understood. Some bats emit a 
short constant frequency (CF) 
signal whose return indicates the 
target's presence and whose 
return frequency can indicate the 
target's speed (see the Doppler 
shift in FC 1.65). Other bats emit a 
frequency modulated (FM) signal. 
The frequency response of the 
target is analyzed to indicate the 
target's shape, size, surface 
texture, and range. Because the 
FM signal is swept over a range of 
frequencies, the bat cannot 
analyze it for a Doppler shift for the 
target speed. Thus, some bats 
emit a combination FM-CF signal 
to obtain all the possible 
information about the target. 

1.67 The fluctuations are not 
quite loud enough (i.e., the 
pressure changes on the ear drum 
not quite large enough) to be 
heard. Even if the Brownian motion 

230 Flying circus of physics with answers 

were more intense, it probably still 
would not be heard because the 
brain will ignore any continuous, 
constant noise signal. 

1.68 Suppose you are talking to 
someone in a social room. You 
hear that person's voice both 
directly and in a diffuse way after it 
has reflected from the room. If 
there are other such conversations 
occurring in the room, there is a 
general diffuse level of talk with 
which your acquaintance must 
compete. The power of that diffuse 
background depends on the 
volume of the room, the acoustic 
absorption of the walls and the 
other objects in the room, some 
characteristic mean free path of 
sound between the walls, and the 
number of other conversations. At 
a critical number of conversations, 
the diffuse background begins to 
drown the direct level of talk from 
your friend. Any additional number 
of conversations means your friend 
will raise his or her voice, but all the 
other people will do the same and 
the party will become hopeless. 

1 .69 Because the rockets 
exceeded the speed of sound, the 
sound from their explosions could 
reach a listener before the sound 
of the flight through the air. 

1 .70 Such a live conversation in 
a noisy party provided at least one 
additional piece of information that 
the tape does not: directionality. 
You can distinguish a particular 
conversation from a very noisy 
background if you can distinguish 
the direction of the conversation 
through your normal binaural 

1.71 Much of the sound you hear 
when you talk, especially the low 
frequency components, comes 

through bone conduction. Others 
hear you without those low 
frequency tones that, to you, add 
fullness to your voice. Listening to 
a tape of yourself on a good quality 
tape player reproduces what 
others normally hear of your 

1.72, You can determine the 
direction of a sound source by 
three means: comparison of the 
intensity, phase, or arrival time of 
the signals at your two ears. 
Intensity differences are useful 
only with short wavelength sound 
because long wavelengths diffract 
around the head to give about 
equal intensities at the ears. 
However, the long wavelength 
sounds will have different phases 
at the ears, the phase difference 
depending on how much from 
straight forward the sound source 
is angled. At intermediate 
wavelengths, corresponding to 
about 4000 Hz, neither technique 
works very well, and determination 
of the source direction is more 

1.73 If an airplane exceeds the 
speed of sound at the height at 
which it is flying, the air it 
compresses will form a shock 
wave. Behind the airplane is a 
cone whose outer boundary is the 
shock wave, As the cone sweeps 
the ground, an observer 
experiences first a pressure rise 
and decline and then another rise 
until normal pressure is resumed. 
The second shock wave is made 
by the planes tail. Sometimes the 
two increases in pressure are 
indistinguishable; other times they 
will come as two distinct booms. A 
shock wave may never reach the 
ground if it is sufficiently refracted 
by the warmer air it encounters 

during its descent. (For similar 
refractions of sound waves by 

variation in the air temperature, 
see FC 1.28 and 1.29.) 

1 .74 Current research is being 
done on thunder production and 
characteristics, The tremendous 
heating of the discharge column in 
the lightning stroke rapidly 
expands the air, creating a 
cylindrical shock wave that is the 
basic noise source for the thunder. 
Near the stroke, one may 
distinguish a hissing, probably due 
to corona discharge (FC 6.46), and 
a click, probably somehow due to 
an upward moving discharge in the 
stroke (FC 6.32). Continuation of 
the thunder (rolls and rumbles) 
may result from echoes of the 
initial sound from the environment. 

1 .75 The attenuation of sound by 
the atmosphere (due to viscosity 
and thermal conduction) is too 
severe for a sound made at a 
height of 80 km or more to reach 
the ground. If the sound is due to 
the collision of ice crystals in one's 
breath, the temperature should be 
at least as low as -4G°C. 

1 .76 Shock waves from the 
artillery cause the visible bands 
because the refraction of the air is 
altered on their passage or 
because there is momentarily 
increased condensation in a cloud 
or fog bank through which the 
waves pass (similar to FC 3.27). 

1.77 The whip crack may be due 

to the slap of the tip against itself or 
from the shock wave as the tip 
exceeds the speed of sound. 

2.1 To simplify the problem, let 
us assume you are wearing a 
rainhat and need not worry about 
the rain on your head. If the rain is 
toward your front or directly 

Answers 231 

overhead, then you should run as 
fast as possible to shelter. If, 
however, the rain is on your back, 
then you should run with a speed 
equal to the horizontal velocity of 
the rain, that is, along with the rain. 

2.2 Experience surely helps 

greatly in the outfielder's ability to 
extrapolate a trajectory. The 
reference suggests that the 
elevation angle may also be of 
help. By running to keep the rate of 
increase in the ball's elevation 
angle constant, the player will 
arrive at the proper place at the 
proper time. The player may have 
this procedure so ingrained in his 
or her playing that he or she may 
not even be aware of the change in 
the elevation angle. 

2.3 Upon approaching an 
intersection whose light has just 
turned yellow, you can stop at a 
maximum negative acceleration, 
race through at some maximum 
positive acceleration, or maintain 
your same speed. For example, let 
us consider the following 
parameters: your car is moving at 
20 mph (30 ft/s) when the light 
turns yellow, the intersection is 30 
ft wide, the duration of the yellow 
light is 2 s, and the maximum 
acceleration is either +10m/s 2 (for 
increasing your speed) or - 10 ft/s 2 
(for stopping). Assuming ideal 
conditions (e.g., that your engine 
instantly responds to a push on the 
acceleration pedal), we can 
calculate the distances to the 
intersection needed for your three 
options. In order to race through 
successfully, you would have to be 
closer than 50 ft when the yellow 
appears. To stop successfully, you 
have to be further away than 45 ft. 
Between 45 ft and 50 ft, you have 
either option. 

2.4 Since the ball is over the 
plate for only about 0.01 s, the 
timing should be to about ±0.01 s. 
The error along the vertical must 
be less than 1 mm. "The 1962 
world championship was finally 
determined by an otherwise 
perfect swing of a bat which came 
to the collision 1 mm too high to 
effect the transfer of title (4)." 

2.5 If the wall is such that you 
cannot just drive around it, and 
assuming ideal conditions of 
brakes, road conditions, and so on, 
and ignoring any considerations of 
how people in the car might get 
hurt for impacts on certain sides of 
the car, then calculations indicate 
that you should steer directly for 
the wall and attempt to stop as 
quickly as possible. Twice as much 
force would be needed to turn the 
car in a circular arc in attempting to 
avoid the wall as would be needed 
to stop the car in a straight stop. 

2.6 In driving, the greatest speed 
will be given to the clubhead for the 
greatest torque you apply to the 
club. For a given torque, however, 
the clubhead speed will depend on 
how the torque is applied. 
According to one study (5), the 
more one hinders the uncocking of 
the wrists, by using a negative 
torque on the wrists during part of 
the swing, the greater will be the 
clubhead speed. The proper 
negative torque and this hindrance 
may be part of the "timing" sought 
by golfers. 

2.7 The beans contain a small 
worm that jumps upward. 

2.8 Apolevaluter must maximize 
the kinetic energy in order to 
maximize the height to which he or 
she travels, but a high jumper 
obtains most of the height from the 

last spring rather than from the 
kinetic energy in the approach. A 
broad jumper may bicycle his or her 
legs to correct an initial forward tilt. 

2.9 Ruth could have hit home 
runs off stationary balls. So, unless 
he was fooled by the ball and 
swung too soon, a slow ball merely 
added to the chances of a home 

2.10 The follow-through will do 
comparatively little damage since it 
is primarily pushing on the 
opponent. The karate strike is 

focused a couple of centimeters 
into the opponent's body, so that 
initial contact is made when the 
striking hand is at its maximum 
speed and thus so that the impact 
force is maximum. 

2.1 1 If the point is to deform the 
struck object, such as in forging, 
then an inelastic collision is 
desired. A greater fraction of the 
hammer's energy will be lost in 
each collision the lighter the 
hammer's mass. So, in forging you 
should use a light hammer. In pile 
driving you want to transfer kinetic 
energy to the pile and avoid any 
loss of energy to deformation. So, 
use a heavy hammer there. 

2.12 The softer the ball, the 
longer it will be in contact with the 
bat, and the more work the batter 
can do on the ball during the 
contact. Thus, follow-through 
should definitely be used on a 

2.13 The optimum bat size would 
be one that requires the least 
energy from the batter to give a 
particular speed to the ball. 
However, batters typically choose 
heavier bats for home runs or 
lighter bats for more ease in 

232 Flying circus of physics with answers 

wielding the bat, giving Jittle 
thought as to the energy imparted 
to the ball. With severaf simplifying 
assumptions, one source (4) finds 
that the optimum bat mass is about 
3.4 times the mass of the ball. 
More exact calculations would 
raise this result but not to the ratio 
of 7 common in baseball or 5 
common in softball, 

2.14 The frictional force from the 
floor is the external force. 

2.15 When the beetle is on its 
back a peg prevents the jump 
muscle from swinging the front half 
of the body upward to initiate 
jumping. Tension is slowly built up 
in the muscle until the peg finally 
slips, and then the rapid rotation of 
the front half of the body hurls the 
beetle upward. Before the beetle 
can jump again, the tension will 
have to be rebuilt. 

2.16 During the falling of the 

sand t each hourglass weighs the 
same in spite of the fact that some 
of the sand is in the air. The 
additional force on one side is due 
to the impact force of the sand. 
What will the balance say when the 
sand first begins to fall or just after 
the last of the sand has hit? 

2.17 Each hole has a different 
cross -sectional area. The same 
cylinder's weight spread over 
different areas will maintain 
different pressures, For example, 
the largest area hole has the least 
weight per unit area, thus requiring 
the least pressure to raise it. 
Therefore, it will regulate the 
lowest pressure in the pan. 

2.18 The large ball collides with 
the small ball after rebounding 
from the floor, transferring its 
momentum and kinetic energy to 
the small ball. The small ball is 

then able to reach a greater height 
than from which it started. The 
maximum gain in velocity for the 
small ball from the collision is three 
times what it has upon reaching 
the floor. Thus, the maximum 
height to which it can return is nine 
times the height from which it was 
dropped. The closer the small 
ball's mass is to the larger ball's 
mass, the less this return height 
will be. 

2.19 The coefficient of sliding 
friction is less than the coefficient 
of static friction. Thus, there is 
greater friction to stop the car if the 
tires turn smoothly on the road 
rather than slide over the road. On 
dry, smooth asphalt the friction 
coefficients for rolling may be as 
much as .8 whereas for sliding ,6 
or less. If sliding begins, the 
asphalt and tire melt and the car 
then skims along on a thin layer of 
liquid. All other things being equal, 
the sliding would require about 
20% more distance than the rolling 
stop. Thus, you will have the 
quickest stop if you apply the 
brakes just slightly less than what 
will lock them, 

2.20 The frictional force on the 
tires does not depend on the 
surface area in contact with the 
pavement, and so a wide slick is as 
effective as a narrow one. If the 
tires are spun over the surface as 
is done in drag racing, then the 
wide tire has an advantage in that it 
has a wider surface to heat and is 
less likely to melt. (Melting greatly 
reduces the coefficient of friction. 
See FC2.19.) 

2.21 The first part of the run is 
limited by the traction with the 
pavement. Greater traction 
reduces the time spent in this part 
but will not affect the final speed 

more than a few percent. That final 
speed will be determined by the 
power limitation of the dragster in 
the second part of the run. 

2.22 The finger that is first 

moved slides beneath the stick 
with a kinetic coefficient of friction. 
The stick does not slide over the 
other finger because the static 
coefficient of friction there is larger. 
The magnitude of friction on either 
finger depends not only on the 
friction coefficient, but also on the 
weight of the stick on the finger. As 
the moving finger is brought toward 
the center, more and more of the 
stick's weight is on that finger. 
Eventually the friction on the finger 
is greater than on the other finger 
in spite of the difference in friction 
coefficients. Then the first finger 
stops and the other finger begins to 
slide, Such an exchange of motion 
can occur several times before 
both fingers are at the center. 

2.23 Sudden braking in a turn 
throws the car forward, decreasing 
the weight on the rear wheels, 
which then are more likely to slide 
outward. Conversely, accelerating 
rocks the car backward to increase 
the rear wheel traction. 

2.24 The initial speed must be 
slow or the maximum static friction 
with the road will be exceeded and 
the tires will slip. Hence, a small 
amount of torque is first needed. 
What gear is best depends on the 
driver's ability and the smoothness 
of the clutch. If the driver always 
spins the wheels in first, the torque 
can be cut in half by going to 
second gear. 

2.25 If left untied, throw a shoe or 
some other article opposite the 
direction you want to go. If the ice 
is ideally frictionless, then the total 



linear momentum of the system 
must remain zero and you will 
therefore slide off. 

2.26 The angular momentum of 
the motorcycle wheels is 
significant and much larger than 
that of the bicycle wheels. To turn 
the motorcycle you lean it The 
torque of the front wheel' s weight, 
calculated with respect to the point 
of contact with the road, causes 
the wheel to precess, thereby 
turning the motorcycle. (Similar 
precession is common in tops. See 
FC 2.69) A bicycle cannot depend 
on precession because the angular 
momenta of its wheels are much 
less. To turn a bicycle you have to 
lean it and also turn the 
handlebars. If you want to turn left, 
for example, do you first turn the 
handlebars to the left or right? 

2.27 The kinetic energy of the 
center of mass of the cue ball (the 
translational kinetic energy) is 
tranf erred, but the cue ball retains 
its rotational kinetic energy. 
Therefore, the cue ball continues 
to rotate just after the collision but 
slips and does not move across the 
table. Eventually the rotation slows 
because of the friction from the 
table and the ball begins to roll. If it 
was originally struck high, it will 
then follow the ball with which it 
had collided. 

2.28 Consider a superball thrown 
at an angle to the floor with some 
spin. In addition to the spin, the 
center of the ball has a velocity 
component downward and one 
parallel to the floor. Collision with 
the floor merely reverses the 
vertical component so that is 
upward afterward. The spin and 
the velocity component parallel to 
the floor change in a more 
complicated way. Consider the 

point of the ball making contact 
with the floor. The sum of its 
velocity around the ball's center 
plus the center's velocity 
component parallel to the floor 
gives the total velocity of this 
particular point parallel to the floor. 
The collision reverses that total 
parallel component of the point, as 
well as changes both the spin and 
the centers parallel component. 
The recoil direction of the ball can 
then be found by determining the 
new full velocity vector of the 
center. For example, suppose a 
ball is thrown to the floor at 45° and 
with no spin. After the collision it 
will move at 23.2 s with respect to 
the perpendicular to the floor and 
with a spin in which the front 
rotates downward. Multiple 
collisions with appropriate initial 
spins account for the several tricks 
shown in the figures. 

2.29 and 2.31 A stable bicycle is 
one whose forkpoint (the point of 
intersection of a projection along 
the front steering axis and a 
horizontal line through the wheel 
center) falls as the wheel turns into 
a lean when the bike is tilted. Of 
the three other designs drawn in 
Figure 2.29b, the third is unstable 
while the second is too stable, 
being too unresponsive to the 
rider's changes of direction. 
Gyroscopic effects have little to do 
with riding stability, although if the 
bike is pushed off riderless, then 
the gyroscopic effect from the 
wheels will help stabilize the bike 
for a while. 

2.30 The oscillatory motion of the 
point of contact between the 
Hula-Hoop and the person keeps 
the hoop moving. That point of 
contact leads the hoop in the trip 
around the person. The initial hoop 

speed should be greater than the 
eventual driving speed. 

2.31 See 2.29. 

2.32 The forces in a spinning 
lasso have apparently not been 
analyzed, and you might try to 
investigate them either 
theoretically or experimentally. The 
short length of rope from the hand 
to the circular section both lifts and 
drags the circular section around in 
a rotational motion. Once a fast 
rotation is created, there is some 
gyroscopic stability due to the 
angular momentum. 

2.33 The rotation about the axes 
of maximum and minimum 
moments of inertia are stable 
against small deviations. Rotation 
about the axis of the intermediate 
moment of inertia is not, and any 
small perturbation sends the book 

2.34 Friction from the stick 
prevents the ring from just falling. 
Part of the stabilization of the 
spinning rings comes from the 
perpendicular force from the stick 
as the ring spins around the stick. 
The spinning rate increases as the 
ring falls because some of the 
potential energy is converted into 
rotational kinetic energy. Since 
nothing has been written on this 
toy, why donl you try some 
experiments or develop some 
models to predict the increase in 
rotational speed? 

2.35 When inverted in water, the 
kayaker extends the paddle and 
pushes toward the bottom to 
provide a torque that rotates 
himself or herself and the kayak 
toward the surface. To maintain 
sufficient angular speed to right 
himself or herself, the kayaker will 
attempt to keep his or her body as 

234 Flying circus of physics with answers 

dose to the axis of rotation as 
poss ble so as to reduce the 
moment of inertia around the 
rotational axis. 

2.36 The car can probably 
produce a certain maximum 
angular acceleration of the wheel. 
The larger the tire's diameter, the 
greater the distance covered in 
each revolution of the wheel, and 
thus the greater the linear 
acceleration of the car. If the car is 
power limited, then adding greater 
diameter tires will decrease the 
angular acceleration, and the car 
will have the same linear 

2.37 The best procedure 
depends on several factors: the 
speed of the spinning as compared 
to the linear speed of the car's 
center of mass, which wheels have 
traction, and whether or not 
stopping the spinning is more or 
less important than stopping the 
linear motion. For example, 
consider that your car has its rear 
spinning to your right, that your 
speed down the road is negligible, 
and that your front wheels still have 
traction. To stop the spinning, you 
should turn your front wheels into 
the spin (i.e., to the right) and 
modestly accelerate the car. The 
torque from the tires about the 
center of mass of the car will 
decrease the angular momentum 
of the spinning. As the spinning 
decreases, ease the front wheels 
back to the left so that you are 
oriented properly on the road once 

2.38 A tire statically balanced 
with a single weight will not be 
dynamically balanced when 
spinning. On the other hand, the 
tire can be dynamically balanced 
and thus have no wobble, but if 

only a single weight is used, the 
tire will still suffer vibrations. The 
usual tire balancing is a 
compromise between the two 
types of balancing. If two weights 
are used, both types of balancing 
can be obtained. 

2.39 The torque you apply by 

pulling on a sheet of paper must 
overcome the torque due to the 
friction between the dispenser and 
the cardboard tube of the toilet 
paper roil. If the required force on 
the sheet is too much, then you will 
tear the paper each time you 
attempt to rotate the roll. The fatter 
the roll, the smaller the force you 
will need for a given torque but the 
greater the torque from the friction 
because of the increased mass. 
The critical radius for most 
dispensers is about 2 cm. 

2.40 A stone that skips on sand 
usually has its trailing edge strike 
first, causing a torque that 
produces both the short hop and a 
rotation to bring the leading edge 
down for contact. After the front 
end strikes, the stone takes a long 
jump. The short hops appear to be 
missing from the skipping over 
water. Again the trailing edge hits 
first, but now the stone planes 
along the water, tilting back as a 
crest develops in front of it, and 
then finally takes a long jump. You 
might try high-speed photography 
to analyze the forces and torques 
more carefully. 

2.41 An inside wheel is not rigidly 
connected to an outside wheel. 
Instead, there is a differential 
between them that, with a set of 
four bevel gears, allows the 
outside wheel to turn faster than 
the inside wheel. 

2.42 A center-mounted engine 

will have less moment of inertia 
about the car's center and will 
therefore require less torque to 

2.43 For a thin rope or wire, the 
walker must constantly oscillate 
left and right, first falling one way, 
then moving the support point 
beneath the center of mass, 
overshooting, falling the otherway, 
then moving the support point that 
way, and so on. Using a pole 
makes the balancing easier. By 
shifting the pole left or right, the 
walker can position the center of 
mass of himself or herself and the 
pole over the wire. With the center 
of mass over the support point, the 
walker is balanced. 

2.44 The ball will orbit around the 
bottle but will not hit it unless the 
ball is swung directly at the bottle. 
There is no torque on the ball 
perpendicular to the plane of its 
orbit, and therefore the angular 
momentum vector perpendicular to 
the plane must remain constant. 
With the bottle beneath the string's 
point of attachment, this 
conservation of momentum means 
that the ball must orbit around the 
bottle except for the direct collision 
swing. You can hit the bottle in a 
sneaky way, however. Twist the 
string before you release the ball 
so that the ball spins while in flight 
and encounters a force such as the 
one used in throwing a curve (see 
FC 4.39). 

2.45 The net angular momentum 
of the cat is constant throughout 
the free fall because there are no 
external torques on it. By 
extending or retracting its legs, the 
cat can make the front half of its 
body have a different moment of 
inertia about its body axis than the 
rear half. For example, if it extends 

Answers 235 

its front legs and retracts its hind 
legs and then rotates the rear half, 
the front half will rotate in the 
opposite direction but not as far. 
So there is a net rotation in the 
direction that the rear half rotated. 
The cat then extends the rear legs 
and retracts its hind legs and 
repeats the process to gain a 
further net rotation in that direction. 
By then the net rotation is sufficient 
that the cat can grab at the floor 
and finally right itself completely. 

2.46 The Austrian turn involves 
rotations similar to those the cat 
uses in righting itself. If there is no 
net torque on the skier, then 
rotation in one sense by the upper 
half of the body must be 
accompanied by a rotation in the 
opposite sense by the lower half in 
order to conserve angular 
momentum. Turning can also be 
caused by shifting one's weight 
forward or backward. Consider the 
first for skiing diagonally across a 
slope. With the center of mass 
forward, the friction on the rear of 
the ski will have larger lever arms 
from the center of mass as 
compared to the friction on the 
front of the ski. Thus, there is a net 
torque on the ski that will rotate the 
ski and the skier. 

2.47 When the yoyo spins at the 
end of the string, the kinetic friction 
between the string and the bottom 
of the yoyo in contact with the 
string is not very large. Suddenly 
moving the string upward 
increases the contact force 
between the yoyo and the string, 
with a sudden increase in the 
friction that may stop the sliding. 
The static friction is more than the 
kinetic friction and thus, instead of 
the sliding then resuming, the yoyo 
wraps itself up the string. 

2.48 I have seen no studies on 
the physics of judo, and you might 
experiment with this question and 
with other aspects of the sport. The 
slapping will increase the contact 
area of the body with the floor at 
the moment of impact, thereby 
decreasing the impact force per 
unit area, a decrease that is 
especially desirable on the rib 
cage. The slap may also rotate the 
trunk of the body away from the 
impact and further protect it. 

2.49 The spinning bullet will act 
as a gyroscope and attempt to 
maintain its spin orientation 
throughout the flight. Therefore 
during most of the parabolic path, 
the wind blows not along the 
bullet's body axis but at an angle to 
that axis. The resulting torque 
causes a precession of the spin in 
the same way a top is made to 
precess. With the bullet slightly 
broadside to the left or right, it is 
deflected from its intended path. 

2.50 The stack will not fall if the 
following rule is met: the center of 
mass of all the books above any 
particular book must lie on a 
vertical axis that cuts through that 
particular book. This must be true 
for each book in the stack. You 
might try determining, either 
theoretically or experimentally, the 
maximum shift possible for a given 
number of identical books. Or, vice 
versa, how many identical books 
are needed for a given overhang. 
For an overhang of 1 book length, 
you need at least 5 books. For 3 
book lengths you need 227 books, 
and for 10 book lengths you need 
1.5 x 10 44 books. 

2.51 The top part of the chimney 
would have less angular 
acceleration than the bottom part 
were it not for the rigid coupling in 

the chimney. Consequently, 
stress develops along the 
chimney's length during the fall. 
The maximum stress during the 
first part of the fall is approximately 
halfway along the length, and it is 
there that the break will most likely 
occur. Should the break occur 
during the last part of the fall, it will 
be approximately a third of the way 
up and due to shearing. 

2.52 Projectiles are deflected by 

the Coriolis force from what should 
be a straight sighting. That force is 
a fictitious one an observer on the 
rotating earth will invoke to explain 
the path of a projectile as the earth 
and the observer turn underneath 
the projectile. Gunners will sight 
their guns to take this apparent 
deflection into account, but the 
extent of the correction will depend 
on the latitude and will be in the 
opposite senses in the two 
hemispheres. The British gun 
sights were set for Britain's 
northern latitude, not for a southern 

2.53 The Coriolis force (FC 2.52) 
also causes a small deflection of a 
river: to the right in the northern 
hemisphere and to the left in the 
southern hemisphere. This 
deflection supposedly increases 
the erosion on those particular 

2.54 The force that increases the 
spin is the Coriolis force (FC 2,52). 

2.55 The right-handed 
boomerang is thrown in a vertical 
plane so that it spins about a 
horizontal axis. Since it is an 
air-foil, there is a sideways "lift" on 
it, the lift being larger on the top 
half than on the bottom half, 
because the top half is turning in 
the same direction that the 

236 Flying circus off physics with answers 

boomerang is traveling, whereas 
the bottom half is turning in the 
opposite direction. Therefore, 
there is a torque attempting to tilt 
the boomerang, but instead of 
tilting, the boomerang veers to the 
left and remains vertical. Sufficient 
veering causes the boomerang to 
turn full circle in its flight. 

2.56 You can pump the swing by 

raising your center of mass (e.g., 
raising your legs) each time you go 
through the lowest point of the 
swing. Your work will add energy to 
the swing and thereby increase the 
amplitude, Starting the swing from 
rest is harder to explain. By leaning 
backward and momentarily falling, 
you gain kinetic energy and give 
angular momentum to the swing, 
you and the swing acting as a 
double pendulum. Upon reaching 
arm's length, you stop your fall, 
and swing with the swing as a 
single compound pendulum until 
you have the opportunity to fall 
backwards again. 

2.57 People fear that the periodic 
pounding of the bridge might 
match a resonant frequency of 
oscillation of the bridge. Although 
each pounding of the feet would 
add only a little energy to the 
oscillation, if there is resonance 
between the pounding and the 
oscillation, the energy will be 
stored and built up, perhaps 
leading to such an extreme 
oscillation amplitude that the 
bridge collapses. (Also see FC 

2.58 The incense swing is 
pumped as is explained in the 
answer to FC 2.56. 

2.59 Imagine an initial single 
bump in the road that sets the front 
end of passing cars oscillating. 

When the front end descends 
during the oscillation, it may force 
the tires to dig in just then. If many 
cars do this at approximately the 
same place, a new bump will 

2.60 The ship's rolling is 90 a out 

of phase with the ocean waves 
striking the ship. The water tank's 
oscillations are at the same 
resonant frequency as the ship but 
will lag the ship's rolling by another 
90°. (Why?) The tank's oscillations 
are therefore a net 180° out of 
phase with the external waves and 
will oppose the rolling of the ship. 

2.61 The pendulum will not 
topple if the vertical acceleration 
due to the oscillation is greater 
than the acceleration of gravity. If 
there is no friction in the pendulum 
system, the pendulum will then 
oscillate to and fro as long as the 
end is still forced to oscillate 
vertically. If there is significant 
friction, then the pendulum will 
assume a stationary vertical 

2.62 You have to choose the 
masses and the length such that 
the frequency of the strictly spring 
oscillation matches the frequency 
of the strictly pendulum oscillation. 
Then, if the system is started in 
one of the types of oscillations, the 
twisting of the spring will feed 
energy into the other type of 
oscillation until there is a complete 
transfer of energy. The transfer will 
then reverse to feed energy the 
other way. 

2.63 A double compound 
pendulum, in which both pendula 
are hinged together, and where 
one has a smaller mass and length 
than the other, will swing together. 
If this is a bell and its clapper, then 

the bell will never ring. One 
solution, and the one apparently 
used at Cologne Cathedral, is to 
greatly lengthen the dapper. 

2.64 The oscillations of the 

balance wheel are near the 
resonant frequency of the swinging 
of the pocket watch. If the watch 
case oscillates with a frequency 
somewhat greater than the 
balance wheel, then the case and 
balance wheel swing in opposite 
phase, and the watch gains time. 
The opposite result occurs for a 
watch case having a lower 

2.65 The dominant frequency 
may result from an acoustic 
standing wave set up in the falling 
water column, much as a standing 
wave can be produced in a tube 
with one open end and one closed 
end. The factor of one fourth 
results from the speed of sound in 
water being one fourth that in air. 

2.66 Vibrational standing waves 
are produced on the bat when the 
ball strikes the places of antinodes. 
This result is undesirable because 
the vibration "stings" the batter, 
wastes energy that could have 
been given to the ball, and may 
break the bat. 

2.67 When the arrow is released, 

it receives a lateral impulse from 
the string and the bow's stock. The 
resulting vibrations cause the 
arrow to snake around the bow's 
stock without touching it, but since 
there is no interference from 
rubbing with the stock, the 
oscillations are around the 
direction of flight, and the arrow 
flies true to the aim. 

2.68 The horizontal and vertical 
vibrations of the notched stick are 
not the same in frequency or 

Answers 237 

amplitude because of the 

difference in shape vertically and 
horizontally and because of the 
pressure from a finger or thumb. 
The resulting vibrational motion of 
the stick, and thus of the pin, is 
elliptical. Depending on the finger 
pressure and on which side the 
stick is rubbed, the elliptical 
oscillations will be either clockwise 
or counterclockwise, and therefore 
so will the pin oscillations. The 
friction between the pin and the 
propeller sets the propeller into a 
corresponding motion. 

2.69 I have no general rules for 
the behavior of tops, although 
some of the equations of motion 
are worked out in the advanced 
mechanics books. An 
asymmetrical top will certainly not 
be stable and its behavior will be 
erratic. A top will precess (i.e., its 
spin axis will rotate around the 
vertical) because of the torque on it 
due to its weight. Superimposed on 
the precession is a wobbling called 
nutation. If the asymmetric top has 
its spin axis initially vertical, it will 
remain there as long as its 
spinning speed is above a certain 
value. Once friction decreases the 
spinning speed below that critical 
value, the top will begin to wobble. 

2.70 The spinning diabolo is in 
essence a top or gyroscope. To 
orient it properly, you must pull on 
the cord in the correct directions. 
For example, if it is spinning 
counterclockwise with its axis 
outward from your body and then 
its far end dips, which way should 
you pull on the cord? You should 
slightly loosen and lower the 
left-hand cord while pulling the 
right-hand cord upward and toward 
you. In this way the torque from 
your pulling will change the angular 

momentum of the diabolo to make 
it horizontal again. 

2.71 The raw egg is not stable 
because it is asymmetric, and it 
therefore cannot rise like the tippy 
tops in FC 2.73. If the shell is 
briefly touched during rotation, the 
fluid inside the raw egg will still be 
rotating and will restart the rotation 
of the shell when you remove your 

2.72 The bottom surface of the 

stones is not exactly ellipsoidal, 
being somewhat slanted toward 
one side. When the stone is 
displaced from its equilibrium 
position by a tap on one end, the 
perpendicular force from the table 
provides a torque that causes the 
celt to rotate. A certain celt will 
rotate in a certain direction 
depending on which way its bottom 
surface is slanted. 

2.73 If the top is spun on a rough 
surface, the friction on the point in 
contact produces a torque that 
precesses the top to an inversion. 

2.74 The mass distribution of the 
moon is not spherically symmetric. 
The earth's gravitational field 
therefore produces a torque on the 
moon that causes synchronous 
rotation of the moon about its axis. 
With such a forced synchronous 
rotation, the moon will always 
present us with the same face. 

2.75 An orbit must be around the 
center of the earth, because the 
gravitational force on the satellite is 
directed to that point. There is no 
way to put a satellite at the 
Moscow latitude so that it remains 
at that latitude because the center 
of its orbit would then not be at the 
center of the earth. 

2.76 Less energy is required with 

the figure 8 path. To reach the 

moon, the ship must at least reach 
the line beyond which the moon's 
gravitational attraction dominates 
the earth's. To reach that line with 
the least energy, the ship should 
stay as close as possible to the line 
through the centers of the earth 
and moon. 

2.77 The moon does primarily 
orbit the sun, just as the earth 
does, the pull from the earth 
causing a perturbation on that 

2.78 A plumb line can be 
deviated from the vertical by 
perhaps several tens of arc 
seconds due to adjacent 

mountains and also due to 
adjacent absences of mass such 
as with a lake. 

2.79 The atmospheric friction 
reduces the total energy of the 
satellite, but only half of the 
decrease in potential energy goes 
into heating. The other half is 
transformed to kinetic energy, and, 
as a result, the satellite has a 
greater speed in spite of the air 
drag. The orbit axis is reduced, of 
course, so this procedure 
continues only until the satellite 
eventually burns up. 

3.1 Assuming the air is trapped 
in the bra, the volume of the air will 
depend inversely on the pressure 
in the plane, which would be less 
than that at ground level and 
therefore would result in a larger 
bra. Had the cabin been suddenly 
opened to the atmosphere, the 
quick reduction in cabin pressure 
probably would have exploded the 

3.2 For the same oven 
temperature more water will 
evaporate from the cake at the 

238 Flying circus of physics with answers 

higher altitude than the lower 
because of the reduced barometric 
pressure at the higher altitude. 
Thus, you will need more water in 
the recipe. Also because of the 
reduced barometric pressure the 
gas inside the cake (consider an 
angel food cake) will cause the 
cake to rise more, perhaps 
increasing the volume beyond the 
strength of the cell walls and 
causing the cake to fall. To avoid 
losing the cake in this way, less 
sugar can be added to decrease 
the production of the internal gas. 
However, rather than decrease the 
sugar and therefore the sweetness 
of the cake, recipes increase the 
flour to obtain the same results. An 
angel food cake will not brown as 
well at high altitudes for the same 
oven temperature because of the 
lower boiling temperature of water 
(FC 3.62). To obtain the same 
browning, high altitude recipes 
increase the oven temperature. 
None of these factors should 
reduce the tenderness of a cake. 
More flour will increase tensile 
strength and thus the toughness, 
but the greater expansion and the 
lower internal temperature (which 
will retard the coagulation of the 
protein) will decrease the tensile 
strength about as much. 

3.3 The cottage does not 
measure the barometric pressure 
but is sensitive to gradual changes 
in the humidity that may 
accompany pressure changes. 
The movement of the figures is 
caused by a twisted piece of catgut 
whose length changes with the 

3.4 Although the general water 
level in a well is governed by the 
local rainfall or snowmelt, changes 
in the barometric pressure can 

vary the water level by several 
inches. When the barometric 
pressure drops during a storm, the 
well level will rise. The resulting 
increased water flow through the 
ground may pick up enough 
sediment to make the water unfit to 

3.5 The smaller balloon has a 
smaller radius of curvature and 
therefore the elastic forces tangent 
to the surface on any small surface 
area have a greater net component 
toward the center of the balloon 
than on the larger balloon. With a 
greater inward force, there will be a 
greater internal pressure. Hence, 
the smaller balloon has greater 
internal pressure. This result also 
explains why a balloon is initially 
more difficult to blow up but 
becomes easier as the balloon 
expands: the components of the 
elastic forces toward the center 
become progressively less. 

3.$ With the greater atmospheric 
pressure at the bottom of the 
tunnel, much of the carbon dioxide 
remained in solution. When the 
dignitaries returned to the surface, 
the gas then came out of solution. 
They had to return underground to 
reduce the release of the gas to a 
tolerable rate, thus indicating to 
what depths drinking can drive a 

3.7 If you do not release air 
continuously during the ascent, 
you will very likely rupture your 
lungs because of the volume 
expansion of the air in the lungs as 
the external pressure on them 
decreases. An ascent from a mere 
15 ft after inhaling air from an air 
tank can be fatal. 

The partial pressure from the 
CO2 in the lungs does not increase 
linearly with time as you ascend 

because you are continuously 
exhaling part of it. The depth of 
maximum partial pressure of the 
CO2 has been determined from the 
following: from the maximum depth 
(where air was inhaled from a tank 
or submarine), expressed in feet, 
subtract 33 ft and then divide the 
result by 2. 

3.8 The air currents are primarily 
due to changes in the barometric 
pressure. If the cave has more 
than one entrance, air may 
circulate between the two 
entrances because of the 
temperature difference between 
the cave's interior and the outside. 

3.9 The tissues of the body will 
not saturate or desaturate at the 
same rate. Consider, for example, 
a dive with an essentially 
instantaneous descent, followed 
by a 30-min stay at bottom and 
then a programmed ascent. Those 
tissues that absorbed the nitrogen 
quickly will desaturate quickly as 
the diver begins the ascent. Those 
tissues that absorbed slowly will 
not initially have as much pressure 
difference between the absorbed 
nitrogen in the tissues and the 
nitrogen in the blood and will 
therefore desaturate much slower. 
Hence, the initial stages of the 
ascent are quick to desaturate the 
fast tissues, and the final stages 
must be slow to desaturate the 
slow tissues. 

3.10 As the hot water heats the 
faucet valve, the valve's metal 
expands and shuts off the water 

3.11 Ice will first form on the 
inside wall of the pipe and 
gradually grow radially until there is 
a solid plug blocking the pipe. Until 
that situation is reached, the 

Answers 239 

expansion of the freezing water 
merely pushes water back into the 
water main, But once the plug is in 
place, further expansion of the 
freezing water between the plug 
and the valve will significantly 
increase the water pressure unless 
the valve is open. If the valve is 
closed, the pipe will eventually 
burst at its weakest point. Hot 
water pipes will be more likely to 
burst because the initially higher 
temperatures decrease the ability 
of the freezing nuclei to initiate the 
freezing, thus lowering the freezing 
temperature. The water in the hot 
water pipe then supercools, that is, 
cools below 0°C, until freezing is 
suddenly and very quickly initiated. 
The resulting rapid expansion of 
the ice plug traps more water 
between itself and the (closed) 
valve, making bursting more likely. 

3.12 The constriction is 
sufficiently narrow for the mercury 
to pass it only under pressure, 
either from thermal expansion or 
from the "centrifugal" force when it 
is swung in an arc. When cooling, 
the mercury thread breaks at the 
constriction because the 
intermolecular forces in the 
mercury are not strong enough to 
pull the upper column of mercury 
back through the constriction. If 
you stick the thermometer into hot 
water, the glass surrounding the 
bulb of mercury will expand before 
the mercury itself. 

3.13 The rubber molecules are 
stretched chains that, when 
agitated by thermal motion when 
the rubber is heated, will pull more 
on their ends and thereby 
decrease the length of the rubber. 
When you stretch the rubber and 
those molecular chains, you do 
work, part of which goes into heat. 

If the rubber is then allowed to 
contract, part of the work done by 
the elastic force decreases the 
internal energy of the rubber and 
thus its temperature. 

3.14 A watch would run at 
different rates when at different 
temperatures were the balance 
wheel not properly compensated 
for a temperature change. 
Suppose the watch is warmed. The 
metallic wheel would then expand, 
have a greater moment of inertia 
about the center, and therefore 
oscillate less quickly and slow the 
watch. However, the expansion is 
compensated such that the 
oscillation is kept approximately 
constant The rim of the wheel is in 
two or three pieces, each having 
one free end and one end mounted 
to a spoke of the wheel. The rim 
pieces are bimetallic. If the 
temperature increases, the free 
end of each rim piece curls inward 
because its metal strips have 
different thermal expansions, the 
strip on the outside expanding 
more and thus bending the rim 
piece inward. This bending inward 
offsets the expansion of the 
spokes. Although the wheel 
changes shape because of the 
heating, its moment of inertia is 
about the same and so are its 

3.15 Under idea* conditions the 
U tube is initially in equilibrium. If 
there is a disturbance from the 
outside, the equilibrium will be 
broken, and the oscillations will 
begin. Suppose the disturbance 
displaces a small amount of water 
from the left to the right. The 
left-hand vertical section then has 
more cold water than the 
right-hand vertical section and the 
denser cold water on the left will 

push into the lighter warm water on 
the right. Eventually the difference 
in water levels on the two sides will 
balance out this difference in 
buoyancy due to the temperatures, 
and the flow will stop. The heating 
and cooling on the tube then brings 
the water back to the original 
temperature equilibrium, the 
buoyancy force is therefore 
reduced, and water flows from right 
to left because of the difference in 
water heights. This procedure 
continues periodically. By 
experimenting you could 
determine how the oscillation 
depends on the size of the U tube. 
You will also notice that the 
reservoir must be larger than some 
critical value or the argument 
above will not be valid. 

3.16 When you pump and 

compress the gas, the 
compression is essentially 
adiabatic (no heat transfer with the 
outside) and the internal energy of 
the air increases, thus increasing 
its temperature. The hot air heats 
the valve. The station's 
compressed air was hot when first 
compressed but since then has 
cooled to room temperature and 
will not heat the valve. 

3.17 The prevailing winds in the 
United States are from the west. 
As the moist winds from the Pacific 
are forced upward by mountains 
(for example the Rocky 
Mountains), the air adiabatically 
coots because of the reduced 
atmospheric pressure and cannot 
retain as much moisture. The 
western sides of the mountains 
therefore receive the released 
moisture. The eastern sides will 
receive comparatively much less. 

3.18 As the winds descend from 
the mountains and into the greater 

240 Flying circus of physics with answers 

atmospheric pressure, the moving 
air is adiabatically compressed and 
thus heated (FC3.16). If the 
descent is rapid, little of this heat 
will be exchanged with the local air, 
and therefore the wind will be 
warmer than the local air. The wind 
will be relatively dry because of the 
answer in FC 3.17. How dry, warm 
winds affect humans is not 
understood, but the positive and 
negative ions in such winds may 
be the source of the irrational 
behavior (FC 6.14). 

3.19 The pressurized gas in the 
bottle rapidly and adiabatically 
expands when the bottle is 
opened, doing work in expanding 
against the atmospheric pressure 
(FC 3. 1 6). The energy for that work 
comes from the internal energy of 
the gas, thereby reducing its 
temperature and causing some of 
the water vapor in it to condense 
out as a fog. 

3.20 The reference suggests that 
the air current over the top of the 
car reduces the air pressure in the 
passenger area, implying that the 
air there had expanded and 
therefore cooled slightly. This 
effect would be similar to the 
cooling of the air in the rapidly 
flowing air stream above an 
airplane wing, an effect sometimes 
made apparent by the fog formed 
above the wing. 

3.21 The winds from the Pacific 
have dumped their moisture on the 
west side of the Rockies lying 
between the Pacific and Death 
Valley (see FC 3.17) and are 
adiabatically heated as they 
descend the eastern slopes (see 
FC 3/18). The hot, dry wind 
entering the valley reduces it to a 
desert. The lack of shade and the 
greater reflection from sand than 

would be obtained from a 
vegetation-covered terrain also 
increases the air temperature just 
above the ground. 

3.22 The air ascending a 
mountain expands and therefore 

cools as it moves into less 
atmospheric pressure. 

3.23 Rising columns of warm, 
moist air cool as they expand in 
their ascent to lower atmospheric 
pressures. The lower temperature 
eventually condenses out some of 
the water to form the clouds and 
also to warm the rising air 
somewhat by the released latent 
heat in the condensation. The 
clouds, therefore, are not held 
together at all, but are constantly 
being formed. Sit sometime and 
watch them form, change, and 

3.24 The atomic fireball very 
rapidly heats the air, which then 
quickly rises, pulling ground-level 
air, dirt, debris, and water moisture 
up in its tail to form the stem of the 
mushroom. As the hot air rises and 
cools by expansion, it eventually 
reaches the temperature of the 
local air and thereafter spreads 
horizontally to form the top of the 

3.25 The cause of the holes in 
the clouds is not well understood. 
One of several explanations is that 
a natural or artificial accumulation 
of freezing nuclei in an altocumulus 
layer quickly brings about freezing. 
The resulting thin cirrus filaments 
further act as nucleation agents, 
spreading laterally to widen the 
hole, while ice crystals fall from the 
central cirrus and thus remove 
water from that area. 

3.26 The air forced upward over 
a mountain expands and cools and 

then condenses out some of its 

water moisture. If the condensation 
occurs just at the mountain top, a 
lenticular cloud will result. If the 
wind is strong, the condensation 
will occur on the leeward side of 
the mountain in the turbulent wake. 
In both cases, the clouds may 
appear to be permanent but are, in 
fact, constantly being created and 

The air forced over the mountain 
may oscillate on the leeward side 
to produce clouds on each upturn 
in the oscillation. These lee waves 
have a wavelength dependent on 
the wind speed and also on the 
change in air density with height. If 
there is little change in air density 
with height, the atmosphere is 
relatively stable, and the lee wave 
oscillations will be slow, giving long 
wavelengths and thus large 
distances between the clouds. 
Large changes in air density will 
cause more rapid oscillations of 
the moving air, resulting in short 
wavelengths and thus short 
distances between the clouds. The 
faster the wind speed, the greater 
the distance will be between each 
upturn of the lee waves; therefore, 
a stronger wind will spread the 

3.27 The rapid heating of the air 
by the blast generates a shock 
wave, with high pressure 
preceding iow pressure. During the 
low pressure the air expands and 
cools, and some of its water vapor 
condenses. After passage of the 
shock wave, the air pressure 
returns to normal, and the cloud 
disappears. Thus, the cloud is 
relatively narrow and expands 
radially from the blast area. 

3.28 Much of the visible light 
incident on the clouds from the sun 

Answers 241 

passes through the clouds and is 
absorbed by the earth. As the 

ground warms, its thermal 
emission (long wavelength light) 
increases. When the clouds 
absorb this radiation, the 
temperatue difference between the 
base and top of the clouds 
becomes sufficient to cause 
turbulence, which then destroys 
the clouds. 

3.29 The mamma are formed 
when a dense cloud layer overlays 
and then descends into a dry layer 
as a downward moving thermal. 

3.30 Fogs are classified into 
several types according to how 
they are formed, Radiation fog 

results when the moist air cools by 
radiating its heat into space and 
condensing out its excess water 
vapor as the humidity increases. 
Advection fog forms when warm, 
moist air flows over a cold ground 
or body of water. The humidity 
does not have to reach 100% for a 
fog to form because in the modern 
atmosphere there are many 
condensation nuclei that will attract 
the water and initiate the fog at 
humidities as low as 60%. Near the 
ocean, these nuclei may be sait 
particles. Near cities they are more 
likely to be the particulate matter 
released by industrial 
smokestacks. The open-coal 
burning of London supplied a great 
many condensation nuclei. Once 
the burning diminished, the 
condensation and the resulting fog 
became less likety. Sometimes a 
thermal inversion (layer of warm air 
overlaying a layer of cooler air) will 
trap industrial pollutants near the 
ground. During such an inversion 
in December 1952 in London, the 
pollution turned the fog that was 
present black and within a few 

days reduced visibility to just a few 
inches. Approximately 4000 
people died from this smog. 

3.31 When your warm breath 
strikes the cold glass, it cannot 
hold as much water vapor and 
droplets form. These drops will 
initiate on condensation nuclei 
either on the glass or in the 
adjacent air. A fresh hot piece of 
toast will "exhale" onto a cool plate 
in the same manner. 

3.32 A vortex is shed by each 
wing so that there is downflow in 
the center behind the fuselage and 
upflow on the outside behind the 
wings on each side. Condensation 
may come directly from the water 
vapor in the engine exhausts or 
from the cooling of the air during 
the vortex motion. Since most 
planes have two prominent wings, 
there will initially be two trails. The 
downflow in the center between 
the two vortex centers decreases 
in momentum as it travels 
downward because of the 
buoyancy force on it upward. To 
reduce its momentum, this air 
decreases in volume, which pulls 
the two vortices closer together, 
eventually making the two trails 
indistinguishable. The speed of the 
descending air increases in spite of 
the decrease in overall downward 
momentum. This downward 
increase in speed will magnify 
irregularities in the trails: the parts 
of the trails descending first will 
descend even more quickly 
because of the increase in speed, 
making those parts appear to have 
burst downward. Soon mixing 
within the vortices reaches the 
cores, and the descent stops. Then 
an underview of the trails may 
show burst popcorn areas 
connected by loops where two 

trails are still distinguishable. 

3.33 The salt apparently acts as 
nuclei for the bubble formation. 

3.34 The air heated by the fire is 
lighter than the cooler air in the 
room and will be pushed into the 
chimney by the cooler air. Once 
the circulation is initiated, it will 
continue even if the chimney is not 
exactly over the fire, The taller the 
chimney is, the better the draft into 
the chimney will be, because a 
taller chimney will hold more warm, 
light air. Consider a parcel of air at 
the entrance to the chimney, just 
over the fire. It is being pushed into 
the entrance by the cooler room 
air, but it is also being pushed 
downward by the air above it. If the 
air above it is warm, however, that 
downward push will be much less 
than the upward push. The more 
overhead hot air there is, that is, 
the higher the chimney is, the 
easier it will be for the room air to 
push each parcel of hot air into the 
chimney. Some chimneys will puff 
if the draft is low and if cool outside 
air periodically pours into the 
chimney top. 

3.35 The hot smoke and gases 
are more likely to rise in the cooler 
evening than during the warmer 

3.36 Initially the hot gases have 
a laminar flow because their 
ascent is relatively slow. During the 
ascent, however, the net upward 
force on them (resulting from the 
buoyancy on the hot gases in the 
cooler surrounding air) accelerates 
them sufficiently that the flow 
begins to break up into eddies. 
Typically the acceleration requires 
about 2 cm to obtain the necessary 
speed for turbulence. 

3.37 The general characteristics 

242 Flying circus off physics with answers 

of a stack plume depend largely on 
the change in atmospheric 
temperature with height near the 
level of the chimney emission. If 
the temperature increases quickly 
with height (a situation that is 
called an inversion), the hot gases 
emitted by the chimney will not be 
able to rise and thus will stream 
horizontally in the wind as shown in 
the first of Figure 3.37a. If the 
temperature decreases from the 
ground to the chimney height and 
then increases for greater heights, 
the gases will not be able to rise 
but can mix downward as in the 
second figure. If the temperature 
decreases moderately with height 
from the ground up, the plume will 
be like the third figure. If there is a 
very marked decrease in 
temperature with height, the plume 
will attempt to rise but can also be 
brought back to the ground in a 
loop by thermal eddies. 

A plume can be split into two 
parts if the breeze is light enough 
not to distort the vortex pair that is 
created as the hot gases leave the 
chimney top. The gas flow in the 
center of the chimney exit is 
strongly upward, but the gas on the 
outside of an emerging puff is 
downward. In a light breeze, this 
pattern splits down the middle to 
form the two plumes as shown in 
Figure 3.376. 

3.38 Ice crystals will grow 
preferentially in one plane, called 
the basal plane, and grow much 
slower along an axis, called the c 
axis, perpendicular to that plane. 
The actual orientations of the ice 
crystals in the ice over a lake will 
vary from place to place and will 
result in different melting rates over 
the lake. An area with mostly 
horizontal c axes will melt such that 
the vertical ice crystals become 

isolated and look like candles 
jutting upward. Lake water seeps 
upward between these candles by 
capillary action to give that area a 
dark appearance. Areas with 
vertical c axes will have larger 
horizontal crystals that melt 
internally to form a honeycomb of 
hollow tubes. These areas will be 
brighter The darker areas absorb 
more sunlight than the brighter 
areas, heat faster, and therefore 
will be weaker and more 
dangerous than the brighter areas. 

3.39 The melting point of water is 
0°C, but the freezing point will likely 
be lower, depending on the purity 
of the water. Very pure water can 
be supercooled (i.e., cooled below 
the melting point without freezing) 
to about -40°C. Impurities will 
initiate freezing at higher 
temperatures (but not higher than 
the melting point), the exact value 
depending on the type and 
concentration of the impurity. As 
the water is cooled, random 
fluctuations in the free energy of 
the system (due to its microscopic 
thermal motion) produce small ice 
islands. If the water is still relatively 
far from the "freezing temperature," 
these islands quickly disappear. At 
"freezing temperature/ 1 the islands 
grow to a certain critical radius 
beyond which they can continue 
growing because the continued 
freezing will lower the free energy of 
the whole system. This critical 
growth will occur at -40°C for pure 
water but at a higher (subzero) 
temperature for impure water, 
because the impurities reduce the 
necessary critical radius of the ice 

3.40 The critical feature is the 
increased evaporation from the 
initially warmer water. If equal 

masses of warmer and cooler 
water are set outside in freezing 
weather and in open-topped 
containers, the evaporation from 
the warmer water will reduce the 
mass remaining in that container. 
With less mass to cool, the water in 
that container can overtake the 
cooling of the initially cooler water 
and reach the freezing point 
sooner. The actual cooling rate can 
depend somewhat on the 
composition of the containers, the 
circulation above the containers, 
and the circulation in the water. 
Although Bacon commented on 
the effect and although the result is 
well known in Canada, people in 
warmer countries find it 
mysterious. The physics journals 
rediscovered it recently only after a 
high school student in Tanzania 
convinced his skeptical teacher of 
the result. 

3.41 Thunderstorms occur most 
frequently in the midafternoon to 
early evening and over land 
masses. A graph of the worldwide 
thunderstorm activity will be 
dominated by the thunderstorms 
over Africa and Europe, making 
the maximum activity at 
approximately 7p.m. London time. 
A graph of the earth's electric field 
(see FC 6.33) will have the same 
shape, with the maximum at about 
the same time, because the 
thunderstorm activity recharges 
the earth, bringing negative charge 
to the ground and positive charge 
to the upper atmosphere by 
lightning and point discharges (see 
FC 6.32 and 6.46). 

3.42 The moisture on your skin 
can freeze to bond your skin to the 
metallic object. The freezing is 
more likely on metal than wood, 
say, because the thermal 


Answers 243 

conductivity of metai is high, and 
your finger tip will be rapidly 
cooled. (See FC 3.78.) 

3.43 Normally the water drains 
from ice as soon as some of it 
melts. With the wet paper around 
the ice, the external heat will have 
to be conducted through the water 
layer, thereby slowing the supply of 
heat to the ice. 

3.44 Water has the greatest 

density when it is about 4°C. Thus, 
when water begins to freeze on a 
pond, the lighter ice floats, the 
water just above freezing rises, 
and the water slightly warmer (near 
4°C) sinks. The surface will 
therefore be colder and will freeze 
first. The surface will also coo! 
faster, because it radiates its heat 
into the atmosphere and because 
the air circulation over the surface 
removes heat. The ground at the 
bottom of the pond is warmer and 
will supply heat to the bottom 
water. The bubbles of relatively 
warm air will supply heat to 
prevent, delay, or decrease the 

3.45 If the snow is near the 
melting point, friction from the skis 
initially melts a thin layer of snow 
on which they can glide. The 
continuous shearing of the water 
layer by the moving skis provides 
the continuous heat needed to 
maintain a water layer. The type of 
material used in the skis, whether 
they are metal or ebonite, does not 
directly matter as far as the initial 
melting goes. However, if the skis 
conduct heat well, as metal skis 
would, the heat will be lost too 
quickly to maintain the water layer. 
Ebonite skis (and the wooden skis 
used years ago) conduct poorly 
enough to maintain the layer. If the 
snow is well below the melting 

point, there will be no water layer, 
and the skis will have to be waxed 
to reduce the friction, 

3.46 Like the skis in FC 3.45, the 
tee skates glide over a thin water 
layer, but unlike the skis the water 
layer is due to pressure melting. 
The weight of a skater supported 
over the two thin blades puts a 
pressure on the ice of 7000 Ib/sq 
in. or more. To know the pressure 
accurately, you would have to 
calculate the weight distribution 
over the actual points of contact 
with the ice, not the total bottom 
surface area of a blade. Other 
materials are unlike water and ice 
in that they do not melt by 
increased pressure as ice does 
and thus could not be used for 
skating. Since skiing does not 
depend on pressure melting, 
presumably you could ski on other 
materials such as dry ice. 

3.47 A sudden warming can melt 
some of the snow to provide 
enough water to lubricate the 
sliding of the remaining snow. A 
sudden cooling can be equally 
dangerous. At sunset, for example, 
the cooling can freeze liquid water 
already present, and the resulting 
11% expansion by the water can 
trigger an avalanche. 

3.48 When you grasp and firm a 
snowball, you pressure melt at 
least the surface, which then 
refreezes to bond the snowball 


3.49 Snow tires are designed to 
bite into snow to increase the 
traction. Studded snow tires 
depend on melting the ice and 
snow beneath each stud by the 
pressure from the cars weight. 
With that weight distributed over a 
smaller contact area, the stud's 

contact area, there is increased 

pressure on the ice and more 
melting. If the snow and ice are 
below 0°F, the increased pressure 
is insufficient to cause melting. 
Sand is useful if pressure melting 
will embed it in the snow and ice 
but, again, that wilt not happen at 
very cold temperatures. 

3,50 and 3.51 When salt is 
added to the water, more heat 
must be removed from the mixture 
to reach freezing, and thus the 
freezing temperature is lowered. 
Not only must the water molecules 
be slowed sufficiently for ice 
crystallization to begin but also for 
them to overcome the adhesion to 
the salt molecules. Salt will also 
raise the boiling temperature of 
water. Because the water 
molecules are attracted to the salt, 
they will have to be moving even 
faster than normal in order to 
escape into the vapor state. Similar 
lowering of the freezing point and 
raising of the boiling point of water 
is behind the use of antifreeze in 
car radiators. 

3.52 The evaporation of the 
water requires heat, which is 
removed from your body if you 
stand wet and nude in a breeze. To 
remove a water molecule from a 
layer of water, in other words, to 
evaporate some water, energy 
must be supplied to that molecule 
to overcome the attraction to the 
other water molecules in the water 
layer. In the meantime, some of the 
water molecules already in the 
vapor state will randomly run into 
the water layer and so return to the 
liquid state and give up energy. If 
both the liquid and vapor are in a 
closed system under equilibrium, 
then as much energy is removed 
by evaporation as is returned by 

244 Flying circus of physics with answers 

condensation. In a breeze, 
however, the water vapor is 
constantly being blown away and 
there will then be a net energy loss 
from the water layer Jf the layer is 
on your skin, the net loss in energy 
will come from your skin, and you 
will feel cool. Methyl alcohol 
evaporates faster than water and 
will cool the skin quicker. The 
porous canvas water bag is cooled 
by the evaporation on the bag's 
surface, especially if a wind is 
constantly blowing across the bag. 

3.53 The fuel evaporation (which 
is enhanced by the increase in the 
air speed when the air is forced 
through the central aperature past 
the fuel jet) takes energy for its 
phase change from the air. As the 
air cools, it can saturate in humidity 
and begin to condense excess 
moisture. If the outdoor humidity is 
between 65% and 100% and the 
outdoor temperature between 25° 
and SOT, then the condensing 
water can freeze on the throttle 

3.54 The brine (salt water 
solution) in the ice blocks is in cells 
that will migrate downward 
because of gravity and also in the 
direction of the higher temperature 
on the block because of 
progressive melting and 
refreezing. Usually the latter is also 
downward since the ice block is 
either floating in the ocean (the 
ocean, which is at freezing 
temperature, is warmer than the air 
above) or on the ground (the 
ground will also be warmer than 
the air). For both effects, the brine 
drains from the block, which 
becomes potable after about a 
year and has nearly no salt after 
several years. 

To understand the drainage 

because of the temperature 
difference from top to bottom on 
the block, consider a vertical cell of 
brine in the block. The salinity of 
the solution will be enough that its 
temperature matches the average 
temperature of the adjacent ice. At 
the lower, warmer end, this salinity 
will be too much (see FC 3.50) and 
there will be melting to reduce it, At 
the upper, cooler end, there is too 
little salinity and there will be 
freezing to increase it. The cell as a 
whole then moves downward, 
eventually reaching the bottom of 
the block. 

3.55 A relatively large amount of 
heat is required to vaporize the 
water in the pan. If the pan is open, 
this heat of vaporization is 

constantly lost as the water vapor 
rises in the air currents. The pan 
top will trap the vapor and thus 
keep that heat in the pan. 

3.56 Other than the one 
reference describing this effect, 
apparently nothing has been 
published on it. Why not try 
experimenting with your own 
oven? Will the increased moisture 
content of the air in the oven mean 
that the air heats any faster? Is 
less heat needed to increase the 
air's temperature by, say, one 
degree? Will the circulation of the 
air change? 

3.57 Often people will prevent 
the freezing of their car radiators 
by similarly placing a lange tub of 
water near the radiator in the 
garage. As the room temperature 
cools and approaches freezing, the 
water will act as a heat reservoir for 
the room. When ice begins to form 
in the tub, a relatively large amount 
of energy (latent heat) is released, 
which will then aid in preventing 
further cooling of the room. 

3.58 The outside air that is 
cooled during the night will flow 
down into the icehouse during the 
early morning as the outside 
begins to warm. This air flowing 
into the icehouse will saturate in 
humidity because of the colder 
temperature there, condensing out 
some of its moisture. The phase 
change from vapor to liquid 
releases a large amount of heat. 
There is less heating of the 
icehouse if direct sunlight is 
allowed to warm the air in it to 
prevent the inflow of fresh air and 
the consequent condensation. 

3.59 The lower, wider end of the 
device absorbs heat from the oven 
and heats the water in the lower 
end of the hollow interior. 
Eventually the water is converted 
to steam, which requires a 
relatively large amount of heat for 
the phase change to vapor state. 
The hot steam rises through the 
tube to the upper end that is in the 
cooler interior of the meat. There 
the water vapor condenses, 
releasing the (latent) heat it had 
abosrbed upon changing to steam. 
The liquid water then runs down 
the tube to begin the cyde again. 
The net heat transfer to the inside 
of the meat is 100 to 1000 times 
faster than the conduction through 
a solid rod of the same metal 
because of the large amount of 
heat involved in the phase 
changes from liquid to vapor and 
then back again. 

3.60 If a mountain were higher 
than a critical height of about 30 
km, the pressure at the base of the 
mountain due to its weight would 
be great enough to liquefy the 
base, causing the mountain to sink 
below the critical height. Hence, 
mountains must be less than about 

Answers 245 

30 km high . Because th e gravitation 
on the Martian surface is iess than 
that on the Earths surface, Martian 
mountains have a greater critical 

3.61 If the demonstration comes 
soon after the first loud sounds 
come from the cauldron, the water 
is not at the boiling temperature 
(see FC 1.12) and, althought hot, it 
should not be dangerous. The 
water breaks into droplets when 
the performer flings it into the 

air. Those drops should cool 
somewhat by the time they reach 
the skin. If the performer is 
sweating throughout the 
performance, as I certainly would 
be, the sweat will protect him from 
the droplets. 

3.62 There is evaporation from a 

body of water even before you 
begin to heat it. Molecules in the 
liquid state having sufficiently high 
energy escape the liquid. Some of 
those vapor molecules eventually 
reenterthe liquid, but there is a net 
loss. As the water is heated, the 
number of molecules in the vapor 
state just above the liquid surface 
increases until finally the pressure 
of this water vapor reaches its 
maximum value, called the 
saturated vapor pressure. The 
corresponding temperature is 
called the boiling temperature. The 
value of the maximum water vapor 
pressure depends on the 
atmospheric pressure. In the 
reduced atmospheric pressure on 
a mountain top, water boils at a 
lower temperature because 
saturation is reached at a iower 
value. Whether or not the surface 
is rolling with boiling bubbles 
depends also on the nucleation of 
water vapor bubbles in the body of 
the water. If the water is especially 

clean and left carefully 
undisturbed, the water can be 
heated to above the normal boiling 
temperature for the existing 
atmospheric pressure. A small 
perturbation, perhaps a dust 
particle, can then cause an 
explosive eruption of boiling. 

3.63 Splashing and capillary 
action puts relatively thin layers of 
water on the edges of the puddles 
or lakes. As that water evaporates, 
the dissolved salt is left behind on 
the edges. 

3.64 The tube connecting the 
birds head and base extends into 
the base. There is a liquid in the 
base that is deep enough to 
submerge the lower end of the 
tube. Above the liquid, both in the 
base and in the rest of the tube and 
the head, is the vapor from that 
liquid. Those two pockets of vapor 
are therefore not connected. As 
water evaporates from the felt on 
the head, the head and the vapor 
inside the head cool (see FC 3.52), 
lowering the pressure of the vapor 
in the head. Then there is greater 
pressure in the vapor pocket in the 
base than in the head and liquid is 
pushed slowly up the tube toward 
the head. Eventually this makes 
the bird so unstable that it tilts 
forward and dunks its head in the 
water glass. Just when the bird is 
horizontal, those two pockets of 
vapor are connected and equalize 
in pressure. With equal pressures, 
there is nothing to force the liquid 
up the tube and the instability is 
removed. During the jostling of the 
dunk, the bird rights itself, and then 
the whole cycle begins again. 

In one study by the RAND 
corporation (1457), large birds 
were considered for use in 
transporting water between 

irrigation canals in the Middle 

3.65 As a water drop approaches 
a very hot skillet, its bottom portion 
instantly vaporizes to provide a 
vapor layer between the skillet and 
the remaining water drop. The drop 
is then heated by radiation through 
the vapor layer, convection 
currents in the layer, and 
conduction by the layer, but these 
three processes will take up to 1 or 
2 min to bring the drop to boiling 
temperature. Thus, the vapor layer 
protects the drop for that long, 
allowing it to dance and skim over 
the skillet surface. 

3.66 Superheated water (liquid 
water hotter than its boiling 
temperature) seeps upward into a 
geyser's cavity and main column 
from heated rock as much as a 
thousand meters below the 
surface. Once the water is in the 
cavity, small vapor bubbles form 
and then grow as they ascend. The 
water through which the bubbles 
pass flashes to steam. The 
resulting pressure forces some of 
the remaining water to erupt into 
the air. This procedure then 
repeats itself, sometimes, as in the 
case of Old Faithful, with a definite 

3.67 In the older-style coffee 
makers, water was placed in a 
bottom container, and then the 
coffee holder was snugly fitted 
over the top with a rubber gasket. 
When the water was heated, the 
air and water vapor above the 
water expanded and pushed water 
up the central tube to pour out onto 
the coffee. After about 5 min, the 
heat was turned off. As the air in 
the bottom container cooled and 
contracted, its lowered pressure 
would allow the outside 

246 Flying circus of physics with answers 

atmospheric pressure to push the 
water through the grounds and 
back into the lower container. In 
many of the modern percolators, 
there are several differences. The 
lower end of the tube is conical and 
fits over the bottom of the pot. The 
water trapped in that cone is 
quickly heated and forced up the 
tube by the air bubbles that are 
released. Were the tube wider, the 
bubbles could not do this. Once the 
water is spilled onto the coffee, 
gravity draws it through the 
grounds and back to the water 
below. Each time water spurts up 
the tube, the tube and cone are 
momentarily lifted, allowing fresh 
(and cooler) water to flow under 
and into the cone. 

3.68 Steam rises through the 
pipe and into the radiator where it 
condenses and then flows back 
down the pipe. The phase change, 
rather than a temperature change 
in the water, releases heat to be 
given off by the radiator. 

3.69 When I do this 
demonstration with the lead, I wet 
my hands first. When my fingers 
enter the molten lead, some of that 
water immediately vaporizes to 
form (at least momentarily) a 
protective sheath around my 
fingers, similar to the protective 
vapor layer in FC 3.65. Normal 
moisture on the skin (especially if I 
am scared and sweating) works 
almost as well. Fire walking 
probably involves protection by the 
moisture on the feet and may 
depend as much on sweating 
between each footfall as having 
callouses on the feet. Although 
having wet feet helps, I find I can 
walk on hot coals with no special 
preparation of my feet. 

3.70 Water hammering occurs 

when water collects somewhere in 
the pipes. When the steam flows 
over the water and suddenly cools, 
the pressure is very suddenly 
reduced. The water is quickly 
drawn into the area of lower 
pressure, striking the pipes with a 
loud thump. To get rid of the water 
hammering, you should drain the 
collected water. 

3.71 The dull side will radiate 
and absorb heat better than the 
shiny side (see FC3.75). 
Therefore, having the dull side out 
might help cook a potato faster and 
then cool it quicker at the table. 
Since apparently nothing is 
published on this effect, why not 
check it? 

3.72 The metal evaporates from 
the filament to darken the bulb. 
Convection currents in the small 
amount of gas in the bulb will carry 
those metal molecules upward to 
darken the top of the bulb. 

3.73 When viewed by a 

dark-adapted observer against a 
perfectly dark background, an 
incandescent blackbody radiator 
becomes visible at about 650 to 
800 K, depending on the angle the 
object subtends in the observer's 
field of view. 

3.74 You might cool yourself 
momentarily by opening the 
refrigerator door, but by then the 
cooling system comes on to 
attempt to cool the interior again. 
More heat is released by the motor 
than is absorbed by the released 
cool air, so the room will become 
even hotter. You can be sneaky, 
however. You can unplug the 
refrigerator as soon as you open 
the door. Of course, then your beer 
will not stay cool, and you will have 
to drink it all. 

3.75 A black surface will absorb 
the radiated heat faster than a 
shiny surface. Thus, the black pie 
pan will heat the pie faster. Glass 
absorbs most of the thermal 
(infrared) radiation incident on it 
and will therefore heat the pie 
faster than the shiny pie pan. 

3.76 Archimedes' feat was 
reconstructed in 1973 by a Greek 
engineer who had 70 fiat mirrors 
(each about 5 ft by 3 ft) held by 
soldiers who focused the sun's 
image on a rowboat about 1 60 ft off 
shore. Once the soldiers properly 
aimed their mirrors, the rowboat 
begun to burn within a few 
seconds, eventually being 
engulfed in flames, Arthur C. 
Clarke independently used the 
idea in one of his science fiction 
short stories ("A Slight Case of 
Sunstroke"). The home-town 
spectators at a soccer match were 
each given a shiny souvenir 
program. When one of the referees 
called an unpopular decision in 
favor of the visiting team, the 
home- town spectators burned the 
referee to a crisp by directing the 
sunlight on him with their 

3.77 The candle converts some 
of the water in the boiler to steam, 
which then pushes the water 
column back through the tube to 
emerge behind the boat in a jet. 
Upon leaving the boiler, some of 
the steam condenses in the cooler 
tube and contracts, thereby pulling 
water back into the tube. However, 
the key feature is that the water 
entering the tube comes from a 
hemisphere of directions, not from 
a single direction. There is a net 
propulsion forward because of the 
asymmetry in the jet emission 
rearward and the inflow from all 

Answers 247 

directions in the rear hemisphere. 

3.78 How cold an object feels 
depends not only on its 
temperature but also its thermal 
conductivity. The quicker a 
relatively cool object conducts heat 
away from your finger when you 
touch it, the colder it will feel. 

3.79 Clothes are needed in hot 
climates to protect the wearer from 
the direct sunlight. Dark clothes will 
absorb more visible and infrared 
light than white clothes, and thus 
white clothes should be worn in hot 
climates. If water is plentiful, then 
the clothes should be porous so 
that sweating and evaporation can 
cool the skin. However, if water is 
scarce, then the clothes must be 
less porous to protect against rapid 
dehydration of the wearer. In 
Herbert's science fiction classic, 
Dune (1460), water is so scarce 
that the desert people wear suits to 
seal in all the precious body 

3.80 The more massive, thicker 
iron pots and pans should have a 
more uniform temperature across 
their bottoms than the modern thin 
steel ones, which will have hot 
spots directly over the burner. 
Sticking is often produced by the 
hot spots. 

3.81 The Northern Hemisphere 
winters are cold not because the 
earth is further from the sun (for it 
is, in fact, closer) but because the 
tilt of the earth's axis shortens the 
days and lowers the sun in the sky. 
Both reduce the amount of heat 
deposited on the surface during 
the day. However, the change in 
temperature will lag behind 
changes in these factors by about 
a month because the ground and 
atmosphere take time to cool. 

3.82 The side of the astronaut 
facing the sun is absorbing thermal 
radiation, which heats the 
astronaut. He is also radiating 
thermal radiation over his entire 
surface area. So, the sunny side of 
his suit will be warm, the shadow 
side cool. (Actually, the suits have 
air conditioning units,) A 
thermometer left in space will 
warm until it is absorbing as much 
radiation as it is emitting. At the 
earth's distance from the sun, the 
thermometer should read 
approximately room temperature, 
depending on how much of its area 
is facing the sun. You experience 
the same thing when you face a 

3.83 The so-called "greenhouse 

effect" is commonly 
misunderstood. Greenhouses are 
not hot because of any radiation 
trapping by the glass, but because 
the cooling by air circulation is 
diminished or eliminated. In fact, 
the glass may reduce the radiation 
flux into the greenhouse rather 
than increase the radiation inside 
by trapping. There is trapping of 
radiation by the earth's 
atmosphere, however, because it 
is more transparent to the short 
wavelength solar radiation than 
the long wavelength radiation. Part 
of the transmitted short wavelength 
radiation is absorbed by the earth's 
surface, heating it, after which 
long-wavelength radiation is 
emitted by the surface. Because 
the atmosphere will not transmit 
that second radiation well, some of 
it will be trapped in the 

3.84 If there is little or no wind, 
most of your heat loss is by thermal 
radiation. Any object with a 
temperature above absolute zero 

will radiate heat, the hotter it is, the 
more it radiates. It will also absorb 
heat from the surroundings, the 
amount available depending on the 
temperature of the surroundings. 
Since your body is almost always 
warmer than your environment, 
there is a net radiation loss. 
Outside on a cold day, or facing 
toward a window with the cold on 
the outside, the absorbed radiation 
is less because of the reduced 
radiation from the environment. 
Consequently, your net radiation 
loss is more, and you feel cold. An 
astronaut space walking without a 
suit in empty space and far from 
the sun should feel a profound 
coldness since there would be no 
environment to radiate to him. 

People can adapt to 
continuously cold conditions by 
adjusting their diet and the rate at 
which blood flows to their skin. 
Eskimos have a higher protein diet 
than do most people living at lower 
latitudes in order to maintain a 
higher basal metabolism to counter 
the cold. To protect against rapid 
heat loss through the skin, the 
capillaries carrying blood to the 
skin contract. If the temperature in 
the limbs drops too much, the 
person will shiver so that the 
increased activity will warm the 

Besides radiation, a person can 
lose heat by conduction (e.g., 
through the feet to a cold ground) 
and by convection, including 
evaporation losses discussed in 
FC 3.52. A fur coat will help keep a 
person warm because the air 
pockets in the fur are very poor 
heat conductors. With increased 
wind speeds, however, the air 
pockets become less effective. 
The best way to wear a fur coat to 
minimize heat losses, especially 

248 Flying circus of physics with answers 

on a windy day, is to wear it inside 
out so that the wind will not destroy 
the pockets of insulating stagnant 
air in the fur. 

3.85 The metal pipe wall 
conducts heat well and would 
constantly be iosing a significant 
amount of heat to the convection 
currents flowing over the pipes. By 
placing a layer of asbestos around 
the pipe, the rate at which heat is 
conducted to the surface to be lost 
to convection is decreased, 
because the asbestos will not 
conduct as well as the metal wall, 

3.86 If the thundercloud is 
several miles away, the wind you 
experience will blow toward it 
because of the updraft in the front 
part of the cloud. When the 
thundercloud is cioser, the wind 
will blow away from it because of 
the downdraft of cold air dragged 
down by the rain. 

3.87 The warmth from the finger 
suddenly decreases the density of 
the fluid next to where the dish is 
touched. The nearby denser fluid 
then displaces the warmed fluid, 
which spreads out over the surface 
until it cools, whereupon it sinks. 
The circulation waves are made 
apparent by the aluminum powder. 

3.88 In the early evening the tree 
is a reservoir of warm air that will 
rise from the tree in a convection 
plume The insects are attracted to 
the warmer air and perhaps also to 
the condensation that may occur in 
the plume as the air cools during 
the rise. 

3.89 The sunlight heats the 
stone on the bottom, and the 
lighter warm water rises in a 
convection plume to the surface. 
The shrimp apparently like the 
warm water (and possibly any 

organic compounds it may carry) 
but do not like sunlight Hence they 
ride the convection current upward 
but steer away from the sunlight 
and, on reaching the sunlit surface, 
descend again, 

3.90 Increased heat flow by the 
blood to the skin surface and 
increased sweating carry off most 
of the additional heat. But these 
can lead to several minor and also 
serious disorders. The increased 
blood flow to the skin may 
decrease the flow to the brain, 
causing faintness, especially when 
a person suddenly stands. 
Nausea, cramps, and circulatory 
failure can result from the salt 
depletion caused by the increased 
sweating. If about 2% of the body's 
water weight is sweated away, the 
person becomes very thirsty. If the 
losses are about 7%, the 
circulation can fail, with the person 
quickly dying. Overheating in the 
body results in the same 
symptoms, leading to collapse and 
possibly death. 

3.91 If you want your coffee as 
hot as possible when class begins, 
add the cream just before class 
because it will cool the coffee. The 
dissolving of the sugar will also 
cool the coffee since energy will be 
used in the dissolving. Stirring will 
cool the coffee because it brings 
warmer fluid to the surface and to 
the walls quicker than the normal 
convection currents would. A metal 
spoon will absorb heat and will also 
conduct the heat out of the coffee 
to be released to the convection 
currents in the air or to be radiated 
to the room. Since black objects 
radiate heat more than white 
objects, white coffee would cool 
more slowly, A similar 
consideration can be made for the 

cup being black or white. The 
relative importance of these factors 
has apparently not been 
determined for coffee. Why not 

3.92 Dye molecules must diffuse 
from the negative through about 
250 microns to the positive, 
arriving in the proper amount of 
processing time (usually a minute 
in today's Polaroid pictures). The 
rate at which the molecules cross a 
given distance will depend on how 
fast they are going which in turn 
depends on the temperature. A 
colder environment slows these 
molecules and thus the diffusion to 
the positive. 

3.93 Cities will be warmer than 
the countryside and even their 
suburbs because of several 
factors. There is less evaporation 
in the city, which would cool the 
city by the loss of the latent heat of 
vaporization (see FC 3.52). The 
paving and building materials store 
more heat than does soil. There is 
usually less wind in cities because 
of the taller and more complicated 
structures. Less important factors 
are the relatively fast snow 
removal in the winter and the heat 
generation by the machines 
(including cars) in the cities. 

3.94 The total kinetic energy of 
the room's air molecules (what is 
called the translational kinetic 
energy) is proportional to the 
product of the number of 
molecules in the room and the 
temperature. With the assumption 
that the air is an ideal gas, it is also 
proportional to the product of the 
pressure of the air and the volume 
of the room. When you heat the air 
in the room, the volume of the 
room certainly does not change. 
Less obvious is that neither does 

Answers 249 

the pressure because the room is 
not seafed and will always have 
leaks to the outside. The room's 
pressure then must be the outside 
atmospheric pressure. As you heat 
the room, both pressure and 
volume remain constant, and thus 
so does the total energy of the 
room's air molecules. But this is 
possible only because as the 
temperature increases, some of 
the air molecules are forced 

3.95 The fruit grower will set up 
pots at the end of the day after the 
ground has warmed from the 
sunshine. The clouds produced by 
the smudge pots absorb the 
thermal radiation emitted by the 
ground and reradiate it to the 
ground. The heat is therefore 
trapped between the ground and 
the clouds, and the orchard does 
not cool as quickly as it would were 
the ground's heat radiated to the 
atmosphere with no return. Natural 
clouds can do the same thing. 

3.96 The snow layer is not a 
good conductor of heat and will 
help maintain the ground's heat by 
insulating it (and the crops) from 
the colder air above the snow. 

3.97 The fires result from the 
visible and infrared radiation 
emitted by the nuclear-blast 

fireball. During about the first 
second after the burst, the fireball 
is so hot (initially about 500,000 K) 
that most of the electromagnetic 
radiation from it is in the ultraviolet. 
But ultraviolet light is readily 
absorbed by air and therefore does 
not leave the immediate area of the 
burst As the fireball expands and 
cools, more of the electromagnetic 
radiation will be in the visible and 
infrared because the shift in the 
emitted radiation will be toward 

longer wavelengths. Both of these 
are transmitted by the air. Their 
intensity about 2 or 3 s after the 
burst will be sufficient to set 
materials such as wood on fire. 
Virtually anything shading a person 
from the direct light from the burst 
can diminish the burning of the 
flesh. There were examples in 
Hiroshima and Nagasaki where 
uncovered skin was badly burned 
whereas adjacent skin shaded by 
the person's clothes suffered 
essentially no burning, 

3.98 An impurity can nucleate 
the crystal growth, serving as an 
initial point of attraction for the 

3.99 The hexagonal structure of 
snowf lakes is determined by the 
hexagonal bonding of the water 
molecules that make up a 
snowfiake. Once the initial crystal 
is formed, water vapor molecules 
will diffuse to and collect on the 
corners of the crystal to begin the 
growth outward to form the 
branches. Why one particular 
pattern is produced instead of 
another will depend on the falling 
speed, the temperature, and the 
availability of the vapor molecules, 
but not in a known manner. Since 
symmetry is so common in 
snowflakes, the conditions for 
adding molecules and branching 
must be the same across the width 
of the flake. 

3.100 Milk rises between two 
nearby Cheerios by capillary 
action, and the surface tension of 
the milk has a horizontal 
component that will pull the 
Cheerios closer. 

3.101 The soil must be broken 
up in order to retain its moisture. A 
packed ground has many small 

openings that will act as capillary 
tubes. As the water climbs to the 
surface, it is lost to evaporation. 
Cultivated ground has much larger 
openings and thus less capillary 

3.102 If the liquid surface curves 

upward on the vertical sides of a 
container, then the adhesive force 
between container molecules and 
liquid molecules is stronger than 
between liquid molecules. The 
opposite is true if the surface 
curves downward on the vertical 
walls. Similar consideration of the 
molecular forces explains whether 
a drop will spread on a particular 
surface or will remain a drop. 

3.103 The atmospheric pressure 
does not push the sap up the trees 
as was thought last century. The 
transport is believed to be due to 
negative pressure. As the water 
molecules evaporate from the 
leaves, and other molecules move 
onto the leaf surface to take their 
place, a strong intermolecular 
force pulls the column of sap 
upward all the way from the roots. 

3.104 See FC 3.106. 

3.105 The rocks rise because of 
the freeze-thaw cycles that occur 
in winter. When the ground 
freezes, the freeze line descends 
through the soil, drawing water 
vapor upward to the line by 
diffusion. When the freeze line 
reaches a rock, it descends faster 
through the rock than through the 
adjacent soil, because of the 
higher thermal conductivity of the 
rock. Therefore, the bottom of the 
rock freezes sooner than the 
nearby soil at the same level. The 
earlier freezing means more water 
vapor will be drawn there to freeze, 
and thus the rock will be pushed 

250 Flying circus of physics with answers 

upward by the expansion of the ice 
beneath it more than the adjacent 
soil will be pushed upward. When 
the ground thaws, loose soil next to 
the rock fills in beneath it to keep it 
in its new position. Many 
freeze -thaw cycles eventually 
brings the rock to the surface. 

3.106 The expansion of the 
freezing water initially just beneath 
the pavement can account for only 
1 1% of the observed "frost heave/' 
The expansion is greatly increased 
by the freezing and expansion of 
water migrating through the pores 
in the soil to the freeze area 
beneath the pavement, if the top of 
the soil is free, the ice 
crystallization will push the ice 
upward to form ice columns 
projecting 1 or 2 in. from the 
ground <FC 3.104). 

3.107 Capillary action draws 
water a certain distance upward 
into the wall. The dissolved salts 
that are deposited at the top of this 
capillary column as the water 
evaporates will draw water further 
up the wall by osmotic pressure. 
The short circuit grounds the 
positive area in this region of 
higher salt concentration to 
eliminate the osmotic effect. 

3.108 Soap bubbles are held 
together by surface tension. 

Because the fluid drains to the 
bottom of the bubble, the top will 
thin quicker and be more likely to 
burst. The air pressure inside the 
bubble is greater than the ambient 
air pressure because part of the 
surface tension is directed toward 
the center of the bubble, thus 
pushing the surface inward. 

3.109 Inverted bubbles, 
sometimes called antibubbles, 
have not been analyzed in much 

detail. Surface tension pulls the 
inner water into a sphere and helps 
prevent the liquid at the two 
surfaces from flowing across the 

air layer. 

3.1 10 If the flame is too large, the 
capillary transport of the fuel to the 
wick's top will be insufficient to 
maintain the flame. Once the flame 
diminishes there is less 
evaporation from the wick, and the 
transport provides more fuel than 
the flame consumes. So the flame 
increases. With a wick of about 2.5 
mm, oscillations occur for wick 
lengths between about 1.5 mm and 
5.0 mm, the shorter lengths giving 
the higher oscillation frequencies 
because the shorter transport 
distance results in a more rapid 
response to the flame changes. 

3.11 1 Because of the great 
increase in the ratio of surface area 
to volume of the individual particles 
as compared to the original lump of 
material, a flame or spark can 
quickly bring the individual 
particles to their combustion 
temperature. The readily available 
air then results in rapid, explosive 

3.112 The screen quickly 
conducts away the flame's heat so 
that the flame cannot extend 
outside the screen. Flammable 
gases may still leak inside to the 
flame, but the volume then ignited 
by the flame is insufficient to 

3.113 When mud dries, it 
contracts, setting up stresses over 
the surface and for some depth 
below the surface. These stresses 
rupture the soil. On the average, 
the intersection of two rupture lines 
should be at right angles because 
the second of the two cracks 

formed should be perpendicular to 
the greatest tension in the first 

3.114 Similar to the mud cracks 
(FC 3.1 13), ice cracks form in the 
contraction of frozen ground during 
a sudden cooling. 

3.115 The exact cause of the 
stone nets is not known, although 
there are several theories. For 
example, frost heave of the ground 
(FC 3.106) may roll an initially 
uniform distribution of stones 
outward to form a circle. Or, if there 
originally was a bare area in the 
midst of stones, that area could 
have absorbed more water than 
the adjacent area and then pushed 
the stones radially outward when it 
froze and expanded. 

3.116 Although this problem is 
popular among physics students, it 
overlooks an important fact: a 
biological system (you, for 
example) is not an isolated system 
under thermodynamic equilibrium 
since it must constantly have 
energy inputs to maintain itself. 
The energy flow through the 
system can organize the system 
and thus reduce its entropy, but the 
overall entropy change of the world 
will increase. The detailed 
mathematical analysis of the 
entropy reduction in a biological 
system is found in current 

4.1 The pressure on the boy's 
finger depended only on the 
density of the sea water and how 
far below the sea's surface the 
hole was. The overall size of the 
ocean did not matter. 

4.2 The further you are below the 
water surface, the more pressure 
there is on your lungs. Around a 
depth of 3 ft the water pressure is i 

Answers 25 1 

large enough to prevent your 
inhaling through a tube to the 

4.3 In order to standardize blood 
pressure readings l they are all 
made level with the heart. If they 
were made, say, at the ankle level, 
then the readings would depend on 
the heights of the people, and the 
results would be more difficult to 

4.4 On the inside of the gate is 
fresh water from the lakes that feed 
the Canal, while on the outside is 
the salt water of the ocean. When 
the pressures are equalized on the 
two sides of the gate, and the gate 
is opened, the fresh water will still 
be higher than the salt water 
because of the greater density of 
the salt water. The higher fresh 
water flows seaward as the levels 
equalize, giving the boat a free 

4.5 Part of the difference in 

ocean levels at the two Canal ends 
is due to the difference in salinity of 
the two oceans. The Pacific is 
saltier and therefore its water 
denser. Using identical reasoning 
as in FC 4.4, the Pacific end of the 
Canal should be lower than the 
lighter Atlantic end, 

4.6 The answer is simple, 
perhaps mischievous. The 
buoyancy on the hourglass must 

certainly be the same in the two 
cases because its volume did not 
change. But with the hourglass 
inverted, it tilts against the side of 
the tube, and friction holds it in 

4.7 The stone in the boat 
displaces a volume of water whose 
weight equals the weight of the 
stone. Since the stone is denser 
than water, it displaces more than 

its own volume of water. When it 
lies on the pool's bottom, it can 
displace only its own volume of 
water. Hence, less water is 
displaced when the stone is thrown 
into the pool, and the pool's level 
must drop. 

In the case of the sinking boat, 
the water level remains the same 
until the boat is fully submerged, 
and then it drops. 

4.8 As the first water pours in 
and fills the first loop, some pours 
over into the second loop. Soon 
that loop fills, and there is an air 
cavity left at the top of the first loop. 
The water flow then stops until the 
water column beneath the funnel 
increases. If that column is 
sufficiently high, then the 
procedure is repeated for the next 
loop. With a limited water column, 
and several loops, eventually the 
column is unable to eliminate the 
air cavities and there is no further 
water flow, 

4.9 The water can be removed 
until there is a centimeter or less 
left between the ship and the dry 
dock walls. The hydrostatic 
pressure from the ship is 
independent of the extent of water 
below or to the sides of the ship. Of 
course, if the water layer becomes 
very thin, then the water will climb 
the walls by capillary action. 

4.10 A submarine can descend 
by taking on water to increase its 
mass. Blowing the water back out 
with compressed air decreases the 
mass for ascension. In order for 
the submarine to be stable while 
submerged, the density of the 
seawafer must increase with depth 
at that level. If the submarine then 
moves upward slightly, a net 
downward force returns it to the 
previous depth. If it moves 

downward, the net force is upward. 
The density depends inversely on 
the water temperature and directly 
on the salinity, both of which 
decrease with depth. Between 25 
and 200 m in depth, a submarine 
can find several layers in which the 
temperature decreases rapidly 
enough with depth to offset the 
decrease in salinity and thus to 
provide stability. 

4.11 If the ratio of the bar's 

density to the fluid's density is 
close to 1 or t the bar floats in 
stable equilibrium as in the first 
figure. If the ratio is some 
intermediate value, then the bar 
floats in stable equilibrium with its 
sides at 45° to the fluid's surface, In 
each case, the orientation of stable 
equilibrium is determined by the 
position in which the potential 
energy of the system is least, 

4.12 Fish use their swim 
bladders to give themselves 
neutral buoyancy so that they do 
not float to the top or drop to the 
bottom of the sea. Suppose a fish 
swims downward. The increased 
water pressure would compress its 
gas cavity. Then, because of the 
decrease in the fish's volume, it 
would have less buoyancy and 
would have to swim in order to 
avoid falling further. Instead, the 
fish secretes gas into its swim 
bladder to keep its volume 
approximately constant. So, in 
spite of the increased pressure, it 
maintains its same volume and 
thus its same buoyancy force. If it 
ascends, the fish reabsorbs some 
of the gas, again to keep the same 
buoyancy force. 

4.13 Two forces hold the 
cardboard in place: atmospheric 
pressure and surface tension. 
Once the glass is inverted, the 

252 Flying circus of physics with answers 

water column descends slightly, 
leaving the air trapped in the glass 
at a lower pressure than the air 
outside the glass. The pressure 
difference between top and bottom 
of the water column provides a 
force to hold the water up against 
its own weight. Additional force is 
provided by the surface tension 
between the water and cardboard 
and between the water and glass. 

4.14 Gas produced in the 
victims" bodies buoys them up. 

4.15 Because the arrangement 
is unstable, any small perturbation 
of the water surface, any small 
wave, will grow quickly in 
amplitude. A bubble develops to 
rise to the tube's top, allowing 
water to fall along the sides of the 
tube. The bubble's upward 
velocity, and therefore the speed at 
which the glass empties, depends 
on the square root of the 
gravitational acceleration (9.8 
m/s 2 ) and the radius of the upper 
portion of the bubble. 

4.16 Both the temperature and 
the salinity of the water decrease 
with depth. As the cold, fresher 
water + rom the bottom rises, it 
warms from the surrounding water 
and then is lighter than the saltier 
top water. Thus, the flow will 
continue. In fact, even without the 
tube it would continue since the 
rising water would exchange heat 
much faster than salt with the 
surrounding water. 

4.17 The instability forming the 
fingers is the same as in FC 4.16. 
The initial motion comes from 
small perturbations, small waves, 
on the surface between the two 
layers of water. The dyed water 
loses heat to the undyed water as it 
descends. That descending water 

will then be denser than the 
undyed water and will continue its 
descent. Undyed water initially 
pushed upward by a small wave 
will warm and then be lighter than 
the surrounding dyed water. Its 
protrusion upward will thus 

4.18 The interface between the 
salt water and the fresh water 
undergoes the same instability as 
in FC 4.15 and 4.17 

4.19 The volume flow rate (so 
many cubic meters of fluid passing 
through a cross section of the 
stream each second) must remain 
constant throughout the stream in 
order to conserve mass. Since the 
water speeds up because it is 
falling, the same volume flow rate 
requires less cross-sectional area 
the further down the stream you 

4.20 The ball is held in place 
against gravity by a pressure 
difference due to the passage of 
the air jet: the pressure beneath 
the ball is greater than that above 
it. The ball deflects most of the jet 
over its top, The pressure in that 
deflected air is reduced, creating a 
pressure difference between top 
and bottom of the ball, (See FC 
4.25 for a similar reduction in 
pressure.) As a result, there is lift 
on the ball. Also as a result, the air 
stream is deflected downward on 
leaving the ball. Since the ball is 
likely to be turning, the Magnus 
effect that deflects a spinning 
baseball (FC 4.39) can contribute 
lift. One possible wrong answer is 
to attribute the lift to a reduced 
pressure in the free air jet just 
because the air is moving. Such a 
conclusion is a misuse of the 
Bernoulli principle. The kinetic 
energy in the air jet comes from 

mechanical work in the machine, 
not from a reduction of pressure in 
the air. The pressure in the free jet 
is, in fact, just atmospheric 

4.21 The ball is suspended by 
the pressure of the air stream on its 
bottom side and gets its stability 
according to FC 4.20. The air 
stream blown into the toy entrains 
air inside the tube, causing an air 
flow from the higher opening to the 
lower one. As the ball passes the 
higher opening, it is merely sucked 
into the tube by the air flow. 

4.22 The water impact supports 
the ball and also supplies its 
stability. Most of the time the ball is 
off center, and the impact forces it 
to spin in a certain direction. Part of 
the water that adheres to the ball's 
surface is carried around half a 
revolution, say, and then thrown 
off. As the water leaves, it pushes 
backward on the ball (in other 
words, there is a reaction force on 
the ball), thereby holding it in the 
stream. Even if the ball leaves the 
stream, some water is still thrown 
off in the next half revolution, and 
the ball returns to the stream as a 

4.23 Apparently nothing more 
than a description has been 
published on this demonstration. 
Why not try experimenting with it? 
What is the pressure just above 
and just below the egg? Does 
turbulence matter? Suppose an 
egg that would float in static water 
were in a narrow, horizontal water 
jet. Would the egg move upstream 
in the jet? 

4.24 The boundary layer of the 
stream next to the spoon develops 
a narrow eddy having reduced 
pressure. With atmospheric 

Answers 253 

pressure on the side opposite the 
spoon and this reduced pressure 
adjacent to the spoon, the stream 
is held against the spoon. (This 
phenomenon is called the Coanda 
effect.) Turning the bottom corner 
is aided by the " teapot effect" of 
FC 4.118. 

4.25 The passage of the air jet 
reduces the air pressure at the 
mouth of the tube. The water 
surface outside the tube is at 
atmospheric pressure. Thus, the 
pressure difference forces water 
up the tube. The real question is 
why there is reduced pressure due 
to the air jet. One wrong answer is 
to attribute a low pressure to the 
free jet- However, as is discussed 
in the answer to FC 4.20, the free 
jet has atmospheric pressure. So, 
the jet must suffer a pressure 
reduction because of its deflection 
by the tube. 

Two factors should be 
considered. Some of the air may 
be forced up and over the top of 
the tube. The air adjacent to the 
tube in this deflected stream would 
move faster and be reduced in 
pressure. If the flow is turbulent, as 
is likely, then the stream develops 
eddies above the tube, which aiso 
reduces the pressure there. Either 
way, the pressure at the tube's top 
is reduced. 

4.26 A high speed train produces 
a high pressure pulse immediately 
in front of itself and a low pressure 
area in its wake. When trains are 
passing, the low pressure area 
between them can suck windows 

4.27 As the air is forced up and 

over these structures, the 
pressures at the tops of the 
structures are reduced (see FC 
4.25). Air can then be pulled from 

the ventilator shaft or the prairie 
dog tunnel, 

4.28 The acceleration of the air 
up and over the front of the car is 
so great that the insects rupture 
from the force. 

4.29 Imagine the flag perfectly 
smooth and fully spread in a strong 
wind. A small perturbation 
develops that, on one side of the 
flag, forces the air outward slightly 
in order to move over the ripple. 
That air stream must speed up as it 
crosses the ripple. The faster air 
has less air pressure, and thus the 
ripple grows because of the 
difference in air pressure on its 
sides: the reduced pressure of the 
air crossing the ripple and the 
normal pressure on the other side 
of the flag. The ripple also moves 
down the length of the flag in the 
direction of the wind, so the flag 
eventually flaps. 

4.30 The wing was tilted 
downward so that it forced the car 
downward and therefore increased 
the traction of the tires on the road. 
With greater traction, the car could 
take a turn faster. The 
aerodynamic force from the wing 
was just like on an airplane (see 
FC 4.31), but downward instead of 

The car with fans in the rear also 
received a downward force to 
increase traction. The air that was 
forced beneath the car had to 
speed up because it was being 
made to enter a restricted opening. 
With greater speed, the air had 
less air pressure according to the 
Bernoulli principle. Hence, there 
was greater air pressure above the 
car than below it, and the car was 
pushed onto the road more. The 
weight of the car was effectively 
increased by about 50%. 

4.31 The air passing the top of 
the wing moves faster than the air 
passing below the wing. The 
pressure above the wing is less 
than the pressure below the wing. 
As a result, a net upward force is 
on the wing. 

Whether or not the Bernoulli 
principle applies to the calculation 
of this lift is not always dear in the 
references. The principle is a 
statement of the conservation of 
energy (here, pressure and kinetic 
energy) along a stream line in the 
air flow. Since the air flow around a 
wing is affected by adhesion to the 
wing and viscosity, both of which 
do work on the air, the principle 
should not be applicable. However, 
it can still be used if the adhesion 
and viscosity are accounted for by 
superimposing a circulation of air 
(forward underneath the wing, 
rearward on top) on the i rational 
flow of the air passing the wing. In 
the work of Kutta and Joukowsky 
on lift, such a superposition of a 
circulation is made. Above the 
wing, the circulation speed adds to 
the i motional speed past the wing 
to give a greater speed. Below the 
wing the circulation opposes the 
irrotiona! flow, and the air speed is 
reduced. By Bernoulli's principle, 
the pressure above the wing is less 
than that below the wing, thus 
there is lift. The application of the 
Bernoulli principle in obtaining lift 
on the wing is therefore somewhat 

The actual lift on a wing is 
calculated in the Kutta- Joukowsky 
theory by determining the 
momentum change in the air 
stream as it is deflected by the 
superimposed circulation. 
According to Newton's law, the 
force necessary to deflect the air 
stream downward is equal to the lift 

254 Flying circus of physics with answers 

on the wing. Some references 
erroneously describe lift on the 
wing but then show an air stream 
that leaves the wing moving in 
exactly its original direction. 

4.32 As the pilot attempts to pull 
out of a dive, the weight of the 
plane effectively increases 
because of the centripetal 
acceleration in the turn upward. 
The lift on the wings, previously 
inadequate, will now have to be 
even larger because of this 
effective increase in weight. To 
gain greater lift, the plane's air 
speed will have to be greater than 

4.33 The passing wind produces 
a "horizontal lift" on the sail toward 
the convex side. (See FC 4.31,) 
This force is most efficient and 
gives the greatest boat speed if the 
boat is sailing 90° to the wind. 

4.34 Normally the frisbee sails 
through the air with its front edge 
upward, thereby gaining lift as a 
wing does (FC 4.31). In addition, 
the frisbee's orientation is 
somewhat stabilized by its rotation, 
just as a gyroscope is stabilized by 
its rotation. 

4.35 There are two types of 

attempts at man-powered flight: 
where planes are powered by men 
and where people (wisely or 
unwisely) leap from tall structures 
flapping their arms and attached 
wings. The latter is unlikely to be 
successful for more than 10 or 20 
ft, with the landing unlikely to be 
soon forgotten. In contrast, 
building lightweight aircraft in 
which one or two people paddle for 
power to lift and propel the craft 
seems promising. The first such 
flight occurred in 1961, lasting for 
about 60 yd. Numerous plane 

designs have appeared since then. 
Wing spans, for example, have 
ranged from 60 to 120 ft. The 
primary concern in these designs 
is to reduce the power necessary 
for lift. Presently, even a good 
athlete cannot power a plane 
beyond about 100 yd. However, 
sporting planes of 50 ft wing span 
and appropriate wing shape should 
be feasible for man-powered flight 
if the plane also takes advantage 
of thermals and wind currents. The 
craft would then be powered by 
one or two people only until it is 
sufficiently high that it can act 
partially as a sailplane (see FC 

4.36 With bottom spin the golf ball 
gains lift in the same way that a 
spinning baseball is deflected 
sideways. (See FC 4.39.) 

4.37 The passing wind pushed 
the cylinders sideways in the same 
way that a spinning baseball is 
deflected in FC 4.39. Appropriate 
orientation of the ship would result 
in the ship moving forward through 
the water. 

4.38 Some of the wind incident 
on the building is forced through 
the opening, having to speed up to 
do so. 

4.39 A curve is thrown by 
spinning the baseball about a 
vertical axis. The passing air then 
exerts a horizontal force (called the 
Magnus effect) that deflects the 
ball. The force on the ball is due to 
the unequal pressures on the ball: 
the side turning into the passing air 
has greater pressure than the side 
turning with the passing air. 

The application of the Bernoulli 
principle is as difficult here as in 
explaining the lift on airplane wing 
in FC 4.31. Again, the principle 

should not apply because the air 
streams passing the spinning ball 
experience both adhesion to the 
ball and viscosity. The side turning 
into the passing air decreases the 
stream's kinetic energy and thus its 
speed. The side turning with the 
passing air increases the air's 
kinetic energy and thus its speed. 
The Bernoulli principle can be 
applied, however, if the effects of 
the adhesion and viscosity are 
accounted for by superimposing on 
the irrational flow of air pass the 
ball a circulation of air that turns in 
the same sense as the ball's spin. 
On one side the irrotional flow's 
speed adds to the circulation flow's 
speed, giving a greater speed. On 
the other side, the two speeds 
oppose each other, giving a lesser 
speed. Since the Bernoulli 
principle now works (because we 
no longer have to include external 
forces doing work on the passing 
air once we superimpose the 
circulation flow), the pressure on 
the first side must be less than the 
pressure on the second side. The 
pressure difference deflects the 

The actual deflection force (the 
horizontal lift) can be calculated 
with the Kutta-Joukowsky theory 
as with the airplane wing (FC 
4.31). Again, some books err in 
their description of the ball's 
deflection by giving the ball a 
deflecting force without giving the 
air stream a deflection. 

4.40 A reverse effect can be 
produced for a slowly spinning, 
slowly moving, smooth ball. Under 
certain conditions, the side of the 
ball spinning with the direction of 
the passing air may remain laminar 
(smoothly flowing) whereas on the 
other side there may be turbulent 
mixing. The pressure in the 

Answers 255 

turbulence would be less than the 
pressure on the other side, causing 
the ball to deflect in the opposite 
way as in FC 4.39. Upon leaving 
the ball, the air stream would, of 
course, be deflected in the 
opposite sense also. 

4.41 The vertical forces initiate 
small amplitude waves. As the air 
passes over these waves 5 it is 
forced upward slightly by the peaks 
and then flows downward into the 
troughs. At the peaks the air speed 
is greater and thus the pressure is 
less. The opposite would be true in 
the troughs if the flow were ideal. 
Such an ideal situation, with low 
pressure on the peaks and high 
pressure in the troughs, would not 
transfer energy from the wind to 
the waves and thus the wave 
would not grow. In the nonideal 
flow the air circulates in a reverse 
direction in the bottom of the 
trough and thereby shifts the high 
pressure point closer to the 
preceding peak. The pressure 
variations are therefore no longer 
in phase with the water wave and a 
net amount of energy is transferred 
from the air to the water. The water 
waves then grow. 

4.42 The monster waves are the 
chance meeting of many ocean 
waves in phase. They are not giant 
waves that traverse the ocean. 
Instead, they quickly disappear as 
the composite waves go off in their 
own directions and leave with their 
slightly different speeds, 

4.43 Wind speeds above about 
5m/s produce water surface 
turbulence that then produces air 

bubbles. Rafts of these bubbles 
are called whitecaps. The group 
velocity of ocean waves is about 
half the phase velocity. This result 
means that individual waves form 

at the rear of a group of waves, 
move foreward at about twice the 
speed of the group as a whole, and 
then disappear at the front of the 
group. The greatest amplitude 
occurs in the center of the group. 
So, each wave in turn moves 
through the maximum amplitude 
position. If that amplitude is more 
than a certain critical value, then 
breaking and subsequent foaming 
occurs. But the foaming will take 
place only when an individual wave 
happens to move through the 
center of the group. Thus, the 
whitecaps will appear periodically 
downwind of each other. 

4.44 A slowly moving boat 
produces bow waves of relatively 
small wavelength. Several of these 
waves will be along the length of 
the ship at any given moment. As 
the boat goes faster, the 
wavelength of the bow waves 
increases until eventually the 
wavelength is equal to the boat's 
iength. Then the bow and stern 
waves reinforce each other, and 
the ship is essentially trapped 
between two crests, one at its bow 
and the other at its stern. For faster 
speeds the resistance from the 
waves increases considerably, 
requiring much more power from 
the boat. The hydroplane avoids 
this problem by lifting the hull from 
the water. Supports extending into 
the water act as airfoils do on 
airplanes: the deflected water 
currents over the moving supports 
give them lift. (See FC 4.31 .) As far 
as the lift is concerned, these boats 
are just airplanes flying through 

4.45 There are two types of 
water waves: capillary waves, 
which are governed primarily by 
surface tension, and gravity 

waves, which are controlled mainly 
by gravity. Longer wavelength 
water waves are of the second 
type; shorter wavelengths are of 

the first type, Neither of these can 
propagate with speeds below 0.23 
m/s. If the beetle skims slower than 
that speed, no wave pattern is 
produced. For faster skimming, the 
beetle creates both types of 
waves. The capillary waves have 
group velocities greater than the 
wavespeed, and they are therefore 
in front of the beetle. The gravity 
waves have group velocities less 
than the wavespeed and thus are 
behind the beetle. Only the 
beetle's capillary waves are 
prominent, but the gravity waves 
are visible with close inspection. 

4.46 Were the ship to generate 
waves of a single wavelength, then 
the angle of its wake could be 
found just as the angle is found 
for the shock wave cone left by a 
supersonic aircraft: sin = civ 
where c is the speed of the sound 
wave and v is the speed of the 
aircraft. In contrast, the ship 
generates waves of a large range 
of wavelengths that travel at 
different speeds. From any 
particular position of the ship, 
these waves are sent outward in all 
directions, the longer wavelength 
waves traveling faster than the 
shorter wavelength waves. 
However, these waves 
destructively interfere except on a 
circle that expands forward in the 
ship's direction of motion. The 
ship's progression leaves a trail of 
these expanding circles of 
constructive interference, the ones 
further back larger than the more 
recent ones. These circles develop 
the V-shaped area in the figure 
such that the angle of this V is 
independent of the ship's speed. 

256 Flying circus of physics with answers 

Consider a particular point on the 
center axis directed from the ship 
backward through the wake. The 
distance from that point to the ship 
is always three times the distance 
from the point to the edge of the 
wake (the outer limit of the 
spreading circles) along a 
perpendicular to the central axis. 
As a result, the sine of the angle of 
the V, and thus the angle itself , 
must always be the same. Inside 
the V the expanding circles of 
constructive interference produce 
the particular pattern of crests 
shown in the figure. 

4.47 Apparently there is no 
published elementary explanation 
for the edge waves. The recent 
publications suggest that they may 
be caused primarily by the 
nonpropagating oscillations near 
the oscillator rather than the waves 
propagated through the basin. 

4.48 The wave speed depends 
on the depth of the water, the 
shallower the water is, the slower 
the waves move. If a wavefront 
approaches the shore at some 
angle, the inshore portion of the 
wavefront slows before the 
offshore portion. As the wave 
progressively slows, the wavefront 
is swung around until it is close to 
being parallel to the shore line (or 
at least the line of shallow water). 

4.49 The front end of the board is 
tilted upward (as the rider assumes 
the characteristic surfing stance by 
leaning backward slightly), and 
water is forced beneath the 
passing board. If the skimming is 
quick enough, then the board 
passes before the water beneath it 
can be squeezed out. For 
example, if the water is 1 in. deep, 
then the water waves wilt move at 
about 0.5 m/s. Thus, skimming 

faster than that speed constantly 
supplies fresh water beneath the 
board to avoid stalling. The force 
supporting the rider is not 
buoyancy, instead, it is the impact 
force from the water. 

4.50 To ride the waves, the 
surfer must move with the wave 
speed. Normally, in deep water, 
the wave speed is greater than the 
speed of the water particles in the 
wave. If the wave is nearly 
breaking, the water has almost the 
same speed as the wave, and the 
surfer needs only a little more in 
order to keep up with the wave. 
The additional speed comes from 
the continuous falling downhill of 
the surfer on the side of the wave. 
Thus, in order to surf, one needs a 
beach with waves that are either 
breaking or almost breaking. The 
water speed is greatest at the crest 
of the wave. Therefore, the speed 
of the rear of the board through the 
water should be less than the 
speed of the front of the board, 
creating an unstable situation. The 
shorter the board, the less this 
difference in speeds is a problem. 

4.51 The bow of the moving ship 
creates a high pressure area in 
front of the ship. The porpoises 
ride between that high pressure 
region and the normal water 
pressure further ahead of the bow. 

4.52 The tides are not due to the 
moon or sun pulling the water 
radially outward from the earth. 
Instead the bulges are caused by 

the horizontal components of the 
gravitational forces from the moon 
or sun collecting the water in the 
bulges. Since the horizontal 
components are less below the 
moon's or sun's position in the sky 
and on the opposite side of the 
earth, the bulges collect there. 

Were the moon to revolve about 
the earth always directly above the 
earth's equator, there would be no 
diurnal (once-a-day) tides. 
However, with the moon's orbit off 
from the earth's equator, some low 
latitude areas can have a dominant 
diurnal tide. 

4.53 The tidal generating force 
depends on the inverse cube of 
the distance to the sun or moon. As 
a result, the moon's effect 
dominates in spite of the fact that 
the sun has a greater gravitational 

4.54 To conserve the total 
angular momentum of the 
earth-moon system, the separation 
between the two increases in order 
to compensate for the earth's loss 
of spin. 

4.55 The wind, barometric 
pressure variations, and seismic 
events oscillate these bodies of 
water. From the range of oscillation 
frequencies in the disturbance, a 
body of water picks out its resonant 
frequency. Standing waves then 
develop in the body of water, just 
as standing sound waves are 
produced in an organ pipe excited 
with a range of sound frequencies. 

4.56 See FC 4.58. 

4.57 The natural period of 
oscillation of the bay is about 13 hr, 
and so the semidiurnal tide forces 
resonant oscillations of the bay, 
much as sound waves can force an 
organ pipe to resonantly oscillate. 
As a result, the bay's oscillation 
energy has been enhanced, and 
the amplitude of oscillation 

4.58 The oore and the sink jump 
are both examples of an hydraulic 
jump, which is a surface water 

Answers 257 

wave anaiagous to an atmospheric 
shock wave, Normal (sinusoidal) 
gravity waves can propagate 
upstream on a moving stream of 
water if the speed of the water is 
less than the speed of the waves. 
(See the answer to FC 4,45 for the 
distinction between gravity and 
capillary waves.) The ratio of the 
stream speed to the wave speed is 
called the Froude number. If the 
Froude number is less than 1 , then 
the stream is "subcritical." If it is 
more than 1, the stream is 
"supercritical." The hydraulic jump 
is a wave that occurs where the 
water flow changes between being 
supercritical and subcritical. There 
is a change in height because the 
wave speed depends on the 
square root of the water depth. For 
example, in the sink hydraulic jump 
the depth is shallow inside the 
circle, the gravity wave speed is 
low, and the flow is supercritical. 
Outside the circle, the depth 
increases, hence the wave speed 
is less, and the flow is subcritical. 
Jn the case of the bore, the inflow 
of tidal water through a channel 
that narrows and rises makes the 
stream supercritical to any wave 
initiated by obstacles in the stream. 
The bore changes the flow from 
supercritical to subcritical by 
increasing the depth of the water 
and thus increasing the speed of 
the water waves. 

4.59 Apparently nothing has 
been published on this 
demonstration. So, you might like 
to experiment with it yourself. 

4.60 The cause of beach cusps 
is still current research. Although 
many theories have been 
postulated, none are generally 
accepted . The larger cusps appear 
to be due to rip current flows, which 

have fairly regular spacing along 
the beach. According to the theory, 
points (horns) of the giant cusps 
are between the rip currents where 
there is least transport of the 
bottom material parallel to the 
shore. The rounded portion (bays) 
of the giant cusps develop where 
the rip currents flow outward to sea 
and thus where there is maximum 
material transport. The cause of 
the smaller beach cusps is not 
known. One of the more recent 
theories describes the incident 
ocean waves creating standing 
waves oblique to the beach. The 
crests and troughs of these oblique 
waves shape the beach into the 

4.61 The rotation of the earth 
causes an apparent force, the 
Coriolis force, to deviate the 
surface flow from the direction of 
the surface wind. This deviation is 
about 45° to the right in the 
Northern Hemisphere and 45° to 
the left in the Southern 
Hemisphere. If the flow is laminar 
(smooth), the deviation increases 
with depth. A plot of the velocity 
vectors with depth is called the 
Ekman spiral. To find the net 
transport through the extent of this 
spiral, one must integrate the flow 
over the depth. The result of the 
calculation indicates that the net 
transport is about 90° from the 
direction of the surface wind. 

4.62 The change of the Coriolis 
force with latitude shifts the 
general circulation of the oceans to 
the west. Since the streamlines in 
the west are then more crowded, 
the current flow there is more 

4.63 When the tea is rotating 

around the center of the cup, the 
centripetal acceleration for such 

circular motion comes from the 
pressure difference between the 
tea nearer the wall and the tea 
nearer the central axis. This 
pressure difference also leads to 
an additional flow, called the 
secondary flow, that deposits the 
tea leaves in the center of the cup. 
Consider two horizontal surfaces 
through the tea, the top layer and 
the bottom layer. In both layers 
there is greater pressure at larger 
radii from the center. But in the 
bottom layer less pressure 
difference is needed to provide the 
centripetal acceleration because 
the friction from the cup's bottom 
prevents the tea from circling as 
fast as it does higher up. In both 
top and bottom layers there is a 
pressure difference, but the 
difference is greater at the top. If a 
small parcel of tea is initially at the 
outer top part of the top surface, 
not only does it circle the central 
axis, but It also descends along the 
wall to the bottom because of the 
pressure difference between the 
outer top and the outer bottom. To 
replace the fluid lost from the outer 
top, there is a flow of fluid from the 
central bottom upward along the 
central axis and then to the outer 
top. Thus, while the tea is circling, 
it is also flowing from outer top to 
outer bottom, to inner bottom, then 
to inner top, and finally to outer top 
again, Tea leaves lying on the 
bottom are captured by this 
secondary flow and deposited in 
the center of the cup where the 
fluid begins its ascent. 

4.64 The secondary flow in the 
preceding problem is also 
responsible for the meandering of 
rivers. Perpendicular to the flow of 
the stream in an initially slight bend 
is a secondary flow circulati ig from 
outer top to outer bottom, then to 

258 Flying circus of physics with answers 

inner bottom, up to inner top, and 
then finally back to outer top. This 
flow removes material from the 
outer stream bed wall and deposits 
it on the inner bed wall somewhat 
downstream. Although a young 
stream may start relatively straight, 
the slight turns in it are enhanced, 
and the stream begins to meander. 

4.65 If the ball is to rise at its 
normal rate, it will have to push the 
water above it outward to the 
sides. But such motion of the water 
will be against the pressure 
difference that keeps the fluid in 
circular motion. (The centripetal 
acceleration of the water in this 
circular motion about the central 
axis is provided by the pressure 
difference between the water at 
larger and smaller radii: there is 
greater pressure on the outside.) If 
the sphere's upward speed is too 
smail to provide this outward 
displacement of the water above it, 
then the sphere ascends with a 
column of water that rises at the 
same rate as the sphere. In other 
words, the sphere pushes and 
pulls upward a column of water its 
own diameter in size. The friction 
on this column and the greater 
mass that is moving both increase 
the time needed for the sphere to 

4.66 The dye displaces some of 
the water when it enters. Part of 
the water is pushed inward toward 
the central axis. But that particular 
parcel of water is now moving too 
quickly for its new radius, and thus 
it tends to press radially outward 
trying to regain its former position. 
The water that is pushed radially 
outward by the drop finds itself 
under too much pressure for the 
centripetal acceleration it has, and 
thus is pushed radially inward 

trying to regain its own old position. 
(The radial pressure difference is 
discussed in the preceding 
answer.) As a result, the dye is 
compressed radially. It mixes 
downward, but stays in a narrow 

4.67 Comments on the direction 
of swirl in a draining bathtub are 
often as strong as in heated 
religious clashes: some people 
argue that all Northern 
Hemisphere tubs drain 
counterclockwise; others insist that 
only about half do. Shapiro (722) 
was the first to carefully test the 
swirl direction, although the 
arguments appear to have 
continued anyway. Unless extreme 
care is taken with a carefully 
designed tub, the rotation due to 
the Coriolis force cannot be seen. 
Normal bathtubs and sinks are by 
no means designed to show the 
Coriolis effect. Swirling in them 
could be in either sense, being due 
to such uncontrolled factors as the 
shape of the tub, the motion due to 
the pulling of the plug, the 
residual vorticity from the filling, the 
air currents above the water, and 
the shape and position of the drain. 
To show the relatively weak 
Coriolis force, you need a very 
symmetric tub with a central outlet 
that can be opened without swirling 
the water. Once the tub is filled, the 
water should sit for about one or 
two days for the vorticity from the 
filling to die out. There should be 
no air currents above the water or 
change in temperature in the room, 
both of which could produce 
motion that would swamp the 
motion due to the Coriolis effect. 
With these and other precautions 
taken, the proper rotation of the 
draining water can finally be seen. 

4.68 The cause, nature, and 
behavior of tornadoes and 

waterspouts are poorly 
understood. Indeed, the distinction 
between the two vortices is not 
clear other than that the 
waterspout is over water, is 
weaker, travels faster, and lasts 
longer. True tornadoes, the type in 
the central plains of the United 
States, are highly destructive and 
accompany violent storms. The 
vertical motion appears to be 
upward through the funnel. 
(Dorothy was carried upward in 
'The Wizard of Oz".) The funnels 
are visible because of the water 
condensation in its low pressure or 
because of the dirt, debris, or spray 
it accumulates from the ground. 
They often occur in the spring 
when the cool, dry air from the 
north meets the warm, moist air 
from the Gulf of Mexico region. 
However, the mechanism that 
generates the vorticity is not 
known. Thermally induced rotation 
may be a cause. Existing rotational 
motion may converge to intensify 
the motion. Super thunderstorms 
may repeatedly produce electrical 
discharges that heat the air so 
severely as to generate the 
vorticity, The frequent occurrence 
of lightning in tornadoes (either 
stroke or ball— see FC 6.32 to 
6.35) makes this latter proposal 

4.69 The granular substance 
promotes the release of carbon 
dioxide gas by acting as nuclei for 
bubble formation. The bubbles 
form in the center of the flow, 
especially if the granular 
substance is dropped there, 
because the pressure in the water 
is less in the center than further 
out. (The pressure distribution is 

Answers 259 

discussed in the answer to FC 
4.63.) The released bubbles 
provide buoyancy to the central 

water, which then rises. Other 
water flows inward at the bottom, 
resulting in a concentration of 
angular momentum in the center. 
The rotational speed increases, 
and the swirl forms. 

4,70 Because of the greater 
density of the cold milk, the milk 
stream descends into the hot 
coffee. Vortex tubes (vortex 
columns) in the rotating coffee 
become entrained in the milk and 
are stretched by the descent. As a 
result, the angular speed of the 
entrained vortices increases, 
perhaps enough to dimple the 
surface. If hot milk is poured into 
the coffee, it will not descend or at 
least wiil not descend as quickly. If 
the hot milk is less dense than the 
coffee, the entrained vortex tubes 
are shortened, and the rotational 
speed decreases. 

4,71, 4.72, and 4.73 The cause 
and maintenance of dust devils are 
not well understood- Apparently 
superheated air initially lies in 
unstable equilibrium near the 
ground. Any small disturbance 
breaks this hot air out of the 
boundary layer so that it may rise. 
Once that break is made, the rising 
hot air will puil other hot air up 
through a chimneylike effort (FC 
3.34). The rotational sense is 
entirely random and does not show 
the preferential rotation as do 
hurricanes. The whirlwinds 
developed above fires and over 
Lake Michigan are similar 
phenomena in that there is very 
unstable hot air beneath cooler air. 

4.74 As a drop enters the water, 
its sides are retarded by the water 
and move slower than its center. 

The vortex forms as the faster 
moving center descends, and 
slower moving edges curl upward, 

The expansion of the ring as it 
approaches the bottom is similar to 
the expansion of smoke rings in FC 

4.75 Vortices are shed from both 
edges of the cardboard in the first 
arrangement. In the second, the air 
is swept along the length of the 
cardboard and then finally breaks 
into a vortex at the trailing edge. 

4.76 The gas initially cools 
because it expands on entering the 
tube. Near the inlet a vortex is 
created that has greater speeds 
near the tube's axis and slower 
speeds closer to the tube's wall. As 
the flow spirals along the tube, the 
speed distribution over the width 
becomes more uniform as the 
inner air does work on the outer air 
due to viscous interaction. As a 
result, the outer region heats by 
the time it reaches the hot air exit. 
The core of the vortex flows toward 
the cold air exit, expanding as it 
passes the inlet and thus cooling. 
So, the increase in temperature in 
the outer layer of the swirl is due to 
viscous work in speeding up the 
outer layer. The decrease in 
temperature in the core is due to 
expansion as it flows in the 
opposite direction. 

4.77 As a bird thrusts downward 
with its wings, it forces an updraft 
beyond the wing that then trails 
beyond the bird. The purpose of 
the V formation is to have another 
bird behind the first to take 
advantage of that trailing updraft. 
Thus, all but the central bird can 
save on energy by using the 
updraft left by the preceding bird. 

4.78, 4.80, and 4.81 The 

behavior of all of these falling or 

rising objects is governed by the 
pattern and changes in the fluid 
flowing past them, but theoretical 
or even qualitative explanations of 
the results are not available. 
Instead, current research has 
attempted to correlate the types of 
behavior with the Reynolds 
number (which is related to the 
presence and degree of turbulence 
in the flow) or some other such 

4.79 The trailing car is propelled 
forward by the vortex flow left by 
the leading car and encounters 
less air drag because the air flow 
has already been diverged by the 
leading car. The whiplash appears 
to occur when the trailing car 
begins to pass. Part of the air 
flowing past the leading car on that 
side is then forced to pass through 
the relatively narrow space 
between the cars, thus speeds up, 
and therefore is reduced in 
pressure. The trailing earthen has 
greater pressure behind it than in 
front on the side closest to the 
leading car. The pressure 
difference accelerates the trailing 
car momentarily as it pulls out to 
pass. The leading car should 
experience a corresponding force 

4.80, and 4.81 See FC 4.79. 

4.82 The fish swim in a manner 
so that, like the birds in FC 4.77, 
they can take advantage of the 
wakes left by their leaders. 
Consider a fish inside the school. 
As it swims it leaves a trail of 
vortices that develop alternately on 
opposite sides of an axis extending 
directly behind the fish. The 
vortices turn such that on the axis 
the water flow is in the direction 
opposite the fish's motion. Were 

260 Flying circus of physics with answers 

another fish to swim directly behind 
this particular fish, the trailing fish 
would have to expend more energy 
because it would be swimming 
against the flow of these vortices. 
However, if the trailing fish were to 
the sice of the axis, it would be in 
the part of the vortex flow that 
moved forward. Imagine two 
leading fish with a trailing fish 
between the two body axes 
extending backwards from them. 
The trailing fish would be in the 
forward moving part of the vortices 
from both the leading fish, and thus 
would have to expend less energy 
than the leading fish in swimming. 
The purpose of the school is partly 
to decrease the energy 
expenditure of all but the leading 
fish by having the trailing fish take 
advantage of the vortex flows of 
the fish in front of them. 

4.83 The wind breaks into 
vortices as it passes the building. 
On the windward side the wind is 
somewhat laminar (smoothly 
flowing), whereas on the opposite 
side the vortices make the wind 

4.84 The large vertical plates on 
the bridge were ultimately 
responsible for the bridge 
oscillations. Such a broad face to 
the wind forced a large amount of 
air to divide and flow around 

the plate and then across the 
bridge. The pressure just above 
and jusi below the plate had 
decreased air pressure because of 
this rerouting and consequent 
speeding up of the passing air. 
Were the plate perfectly symmetric 
in the wind, the decrease in 
pressure on top and bottom would 
have been the same. However, the 
wind blew at fluctuating angles to 
the plate, and thus the pressures 

were different from moment to 
moment This pressure difference 
flowed across the width of the 
bridge and was augmented by the 

turbulence shed by the windward 
plate. As a result of the pressure 
difference between top and 
bottom, the bridge began to 
oscillate. Similar oscillations are 
also developed in "galloping" 
telephone wires, where the 
pressure differences and vortex 
shedding also produce a whistling 
from the wires (FC 1.55). 

4.85 Clear air turbulence (CAT) 
appears to be due to what is called 
Kelvin-Hefmholtz instability. As a 
model of the instability, consider a 
dense and a light fluid in a basin 
with the lighter fluid on top and with 
the two fluid layers sliding over 
each other. If their relative speed is 
slow, any small disturbance in the 
interface is quickly eliminated. For 
greater speeds, however, a 
perturbation in the interface can 
result in an intrusion of one fluid in 
the other where the intruding fluid 
then develops a swirl, Similar 
vortex development can occur in 
the atmosphere where there is 
strong vertical wind shear (and 
thus relative motion of two layers) 
and large horizontal temperature 
gradients (and thus differences in 
densities of adjacent layers). The 
CAT is thought to be swirls 
developed at the interface. 

4.86 Because there is reduced 
air pressure on the mountain tops, 
the air viscosity is less there, and 
thus the watch should run faster. 

4.87 The mesh introduces 
turbulence and cavitation in the 
stream because it narrows the 
aperture through which the water 
passes. The sensation of softer 
water is probably due to the air 

bubbles that are formed. 

4.88 To my knowledge there has 
been no systematic research on 
this question, although sports 
articles often refer to fast and slow 
pools. I could guess that the 
gutters designed to absorb surface 
waves would eliminate the 
reflected waves that may interfere 
with swimmers. Why not research 
this and other aspects yourself? 

4.89 A stream passing over a 
spillway is similar to an air stream 
passing an edge (FC 1.56) in that 
oscillations are created in the 
stream. In the falling water the 
oscillations set up a standing wave 
with five-fourths wavelength from 
the spillway to the ground. 
Because of the resonant feeding of 
energy from the pressure 
variations induced by the edge to 
the oscillations of the falling 
stream, those oscillations can grow 
to a significant amplitude. This 
standing wave may be related to 
the earth's vibrations near a water 
fall (FC 2.65). 

4.90 As the air passes the outer 
edge of the parachute, vortices are 
shed. Since the shedding 
alternates from one side to the 
other, and since they each have 
reduced air pressure, the chute 
experiences lower pressure first on 
one side, then on the other. This 
alternating of pressure begins to 
swing the parachute. If the 
oscillation frequency is close to the 
resonant pendulum frequency of 
the parachute and its load, the 
oscillation can be as large as 60°. 
The central hole allows some of 
the incident air to continue along 
the central axis of the parachute 
and break up the vortices on the 
top side. Stock cars can tolerate 
the oscillations even less than 

Answers 26 1 

parachutists, so the parachutes on 
the cars have even more direct 
flow areas to further reduce the 

4.91 The explanation of the boat 
drifting faster than the stream is 

stil! missing details about the water 
flow and momentum transport near 
the boat. However, the higher boat 
speed is partially justified by a 
simple analysis of the forces on the 
boat. Its weight is directly down, 
but the buoyancy is at an angle to 
the vertical, because the river is 
flowing downhill. Thus, there is a 
component of the boat's weight 
that is parallel to the stream's 
surface. This component is 
balanced by the drag from the 
water. An equivalent volume of 
water in the boat's place would 
experience drag also. But because 
of turbulent mixing in such a 
volume of water, it would meet 
greater resistance than the solid 
boat does at the same speed. As a 
result, the speed at which the drag 
cancels the parallel component of 
the weight is greater for the boat 
than for an equivalent volume of 

4 . 92 A so I i d fen ce create s strong 
vortices that swirl the snow. A 
fence, on the other hand, creates 
milder vortices. If the air speed in 
these fence vortices is less than 
that needed to suspend the snow, 
then the snow is deposited on the 
leeward side of the fence. 

4.93 In order for an obstacle to 

capture the snow, the snow has to 
be brought nearby. The wind 
begins to diverge tens or hundreds 
of meters in front of a large house, 
thus diverting the snow too early 
for it to be deposited at the house. 
A smaller obstacle, such as a pole, 
diverts the air much less, and the 

snow can get near. 

4.94 The trailing edge is sharp so 
that the boundary layer on the top 
of the wing does not separate 
prematurely. Such a sep ration 
would result in turbulent mixing at 
the rear of the wing, which would 
put the airplane in stall because it 
destroys the lift, 

4.95 The aerodynamics of a 
skier are, of course, too 
complicated for an exact 
theoretical solution, so the choice 
of a particular stance without 
experimental data is largely just a 

4.96 The air drag on the ball 

comes from two factors: the 
pressure difference between front 
and back sides of the ball, and the 
friction between the air and the 
ball. With a smooth ball the 
boundary layer of air on the ball 
separates from the ball without 
entering the rear side much. After 
separation, the air develops 
vortices and leaves the rear in 
reduced pressure. Since there is 
higher pressure on the front side, 
the pressure difference retards the 
ball. A rougher surface delays the 
separation of the boundary layer. 
As a result, there is less pressure 
reduction on the rear side, less 
pressure difference between front 
and rear, and therefore less drag 
due to the pressure difference. The 
dimpled golf ball goes further, 

4.97 There are two general 
aspects to a bird's ability to fly. Its 
wings act as airfoils (FC 4.31), and 
the bird can soar (FC 4.98). But 
when it flaps its wings to propel 
itself, the thrust comes not from 
pushing backward on the air, but 
from the feathers twirling in the air 
and acting as propellers. Perhaps 

a plucked bird could soar, but it 
could not propel itself. 

4.98 Birds and sailplanes can 
soar by two techniques. They can 
fly into wind that is deviated 
upward by some obstacle such as 
hills and water waves. More 
practical for distance flying, 
however, is for them to fly into 
rising bubbles of hot air. Once lifted 
by such a bubble, they can then 
glide downward until they find yet 
another rising bubble. The bubbles 
are not tall columns of hot air. 
Instead, they are ring vortices that 
are developed as hot air in the 
boundary layer of air on the ground 
breaks loose from the ground. The 
circulation in the ring is upward in 
the center and downward on the 
outside (an upside down version of 
the vortices in FC 4.74), A bird can 
soar by circling around in the rising 

4.99 AH kites act essentially as 
airfoils in that they force the air to 
diverge and there is less pressure 
on the top than on the bottom to 
give lift to the kite (see FC 4,31). 
The different bridling techniques 
distribute the stress from the 
handling string and also give 
stability to the kite. For example, 
the last three techniques shown in 
the figure will give a stabler flight 
than the first technique. The 
bridling can also be used to adjust 
the kite's angle of attach, that is, its 
angle with respect to the wind 
direction. In a light wind, the kite 
should be at more of an angle to 
the wind so as to diverge more air 
to get the proper lift. With stronger 
winds, the kite should be at less of 
an angle since less wind needs to 
be diverted, A kite tail has two 
purposes other than just being fun 
to watch. Its air drag stabilizes the 

262 Hying circus off physics with answers 

kite, thus making the kite less 
subject to gusty winds. And, 
second, the drag helps adjust the 
kite to the angle of attack proper to 
the prevailing wind. 

4.100 Cloud streets are due to 
longitudinal vortex rows, that is t 
rows of vortices whose axes of 
rotation are horizontal and in the 
direction of the wind. Where the 
circulation is upward between two 
adjacent rows, the air cools by 
expansion and condenses out 
some of its moisture to form a 
cloud (see FC 3.23). No cloud is 
formed where there is downward 
motion between two adjacent 
rows. The vortices are produced by 
a thermal circulation in which 
warmer air rises and cooler air 
descends, similar to the Bernard 
circulation cells of FC 4.101. The 
horizontal wind stretches these 
vortices so that they become 
horizontal vortex rows, 

4.101 If the bottom fluid is 

sufficently hotter than the top fluid, 
the fluid is unstable and convection 
currents of rising hotter fluid and 
descending cooler fluid can 
develop into these patterns. For 
example, the hot fluid can rise in 
the interior of a hexagon while cool 
fluid descends on the boundary 
with other hexagons. For a given 
temperature difference and a given 
fluid, theory can determine those 
patterns (rolls or hexagons) that 
are steady-state solutions of the 
flow. Part of the visible appearance 
of the cells on the coffee is due to 
tiny drops suspended just above 
the areas of rising coffee, A 
charged comb disturbs these 
drops and partially destroys the 
cellular appearance. 

4.102 The dune streets are due 
to the same type of horizontal 

vortex row formation in the air that 
is responsible for the cloud streets 
in FC 4.100. Where two adjacent 
rows have ascending air, sand 
collects in a dune street. Where 
two adjacent rows have 
descending air, there is no dune. 
Since the dominant winds in all the 
world's deserts are north or south, 
the streets run north and south. 
Similar rows develop on the 
surface of the ocean because of 
similar vortex rows in a layer of 
water beneath the surface. Where 
two adjacent rows have 
descending water, material such 
as seaweed collects. There is a 
corresponding absence of material 
where two adjacent rows have 
ascending water. Although the 
dependence of these vortex rows 
on the direction and strength of the 
wind is well established, their 
actual production mechanism is 
not known. 

4.103 To explain the expansion 
of a ring as it approaches a wall, 
imagine a mirror-image ring 
approaching from inside the wall at 
the same time. The parts of each 
ring's flow that are perpendicular to 
the wall cancel. The parts of their 
flow that are near the wall and 
parallel to it add. As a result, the 
ring expands parallel to the wall as 
it gets closer to the wall. Of course, 
there really is no second ring inside 
the wall, but the airflow caused by 
the presence of the wall is the 
same as if there were a 
mirror-image ring. 

In spite of the descriptions of 
multiple passages of smoke rings 
in the literature, the trick may be 
impossible. Until 1972 those 
descriptions were common in 
some textbooks, but then 
Maxworthy (850) carefully 
investigated the effect with water 

rings. If the rings initially have 
almost equal speeds, then the rear 
one merely becomes entrained in 
the leading one to form a single 
vortex ring that does not separate. 
However, if the rear one initially 
has a much greater speed than the 
leading one, the composite ring 
becomes unstable and throws the 
former rear ring forward, leaving 
the former leader behind. The 
former rear ring then has the same 
or a somewhat greater speed, 
making a future encounter 
between the rings unlikely. If 
Maxworthys descriptions are 
complete, then the 
multiple-passage descriptions are 
an example of where textbooks 
have continued to use an 
illustration that no one bothered 

4.104 On an initially flat sand 
floor, the wind picks up and then 
drops sand grains, which then 
cause other grains to hop up. The 
result is to build deposits of sand 
that in turn modify the wind to 
further enhance the deposits. 
Ripples develop with a wavelength 
about equal to the average 
distance a sand grain hops when 
struck by other sand grains. 

Sand waves on stream beds 
may be built in a similar way, or 
they may result from the flow of 
vortex rows (see FC 4.100 and 
4.102). In the latter case, the sand 
ripples are oriented along the 
direction of motion of the stream's 

4.105 Contrary to much popular 
belief, the fluid is not pushed over 
the siphon by air pressure, as is 
disproven by the fact that siphons 
can operate in a vacuum. The 
force that pulls the fluid over the 
siphon is its own intermolecular 

Answers 263 

force. When the siphon works, 
there is more fluid on the outiet 
side than on the inlet side, and the 
resulting imbalance of weight 
causes the fluid to flow up, over, 
and then down the siphon. As the 
fluid travels up the inlet side, its 
pressure is reduced the further up 
it goes, If the siphon is high 
enough, the fluid pressure is 
eventually reduced to the point 
where bubbles (of air or other 
gases) begin to form. Such bubble 
formation limits the height of the 
siphon because it breaks the 
intermolecular bonding between 
the fluid molecules and destroys 
the siphoning. Siphons work better 
at atmospheric pressure than in 
vacuum, because the pressure on 
the two ends of the siphon 
increase the fluid pressure at all 
points in the siphon. Thus, with 
atmospheric pressure outside the 
siphon, the height at which bubble 
formation occurs is increased. 

4.106 The wind (which flows 
down and to the left in the diagram) 
picks up sand grains on the 
windward side of the dune and 
then dumps them as it spills onto 
the leeward side. Although slow, 
the net transport of the sand 
results in the dune formation 
moving downwind. 

4.107 All modern toilets have a 
siphon between the toilet bowl and 
the plumbing to the sewer. As 
water is put into the bowl, the water 
level in it and the inlet side of the 
siphon rises. Eventually water 
spills over from the inlet side to the 
outlet side of the siphon and the 
siphoning begins. (You can flush a 
toilet by just pouring a bucket of 
water into it.) The siphoning flow 
and the general swirling of the 
water pouring into the bowl remove 

the waste. The extra hole at the 
bottom of many bowls is a water jet 
that entrains the fluid from the bowl 
and increases the speed and vigor 
of the siphoning, 

4.108 As an oil drop is released 
from a car, air resistance stretches 
it out, inflates it like a chefs hat, 
and then bursts the center of that 
inflated shape. When the oil strikes 
the road, it is doughnut shaped. 

4.109 These lines are small 

ridges pushed up by the viscous 
forces of the stream flowing 
beneath surface films (e.g., an oil 

4.110 Nothing beyond a 
description of the clear band has 
been published. You might try 
experimenting with different fluids 
and solutions to understand this 

4.1 1 1 The oil forms a very thin 
film over the water. The surface 
tension of such a film is not 
constant, instead it changes as 
the film stretches and contracts. 
Waves passing over the film 
alternately stretch and contract the 
film and so produce an alternating 
tangential drag on the water below 
the film. This drag increases the 
energy loss of the wave to such an 
extent that the wave damps out 
quickly, leaving the film-covered 
area calm. 

4.1 1 2 Oil films on the water 
surface collect and then damp out 
small waves to give streaks or 
patches of calm water. (See the 
preceding answer.) Apparently the 
oil comes from diatoms that have 
oil for assistance in flotation and for 
food. If the wind is strong, the oil 
patches arrange themselves in 
rows as is discussed in the answer 
to FC 4.102 

4.113 Both the crown and the 
central breakup of the central jet 
are due to an amplification of 
unstable waves on the water. In 
the crown case the wave is around 
the rim. 

4.1 14 The surface tension of the 
water holds the water in a thin layer 
and eventually pulls it back to the 
central support beneath the disc. 

4.1 15 If the two water jets are 
exactly identical, then the vertical 
components of their momenta are 
canceled in the collision, and the 
pressure developed at the point of 
impact sends the thin water layer 
out horizontally. Breakup occurs 
when small holes develop and are 
then enlarged by the water's 
surface tension. 

4.116 Surface tension holds the 
streams together. 

4.117 The surface film on which 
the pepper grains reside contracts 
as the soap film develops and then 
spreads across the surface. 

4.118 The turn of the stream 
around the edge of the can is 
stable because of the pressure 
difference across the width of the 
stream. An ideal incompressible 
fluid in a circular path has greater 
velocities at smaller radii. Thus, by 
the Bernoulli principle, there is less 
fluid pressure at smaller radii. Here 
the atmospheric pressure outside 
the stream is greater than the fluid 
pressure near the edge and 
therefore holds the stream to the 
edge. At some point on the side of 
the can the stream detaches 
because it is unstable to small 

4.119 Previous to Loewenthal's 
work the tears forming above 
strong alcoholic drinks were 

264 Flying circus of physics with answers 

thought to be due to surface 
tension pulling the solution upward 
along the glass where then the 
alcohol would evaporate to leave 
just water. However, Lowenthal 
demonstrated that the water 
collecting at the top of the climbing 
film was condensation from the 
room air. Furthermore, the force 
responsible for the film's climbing 
was not surface tension pulling the 
film up but a pressure that 
developed in the fluid next to the 
glass surface. 

4.120 There are several tire 
designs to decrease the probability 
of aquaplaning. The tread can 
channel the water at the rear of the 
contact area outward and eject it. 
Other, shorter channels can eject 
water to the sides. Finally, small 
holes in the tire can essentially blot 
up a water layer as they make 
contact with the road in the front 
part of the contact area. In each of 
these techniques the emphasis is 
on removing the water quickly to 
avoid aquaplaning. 

4.121 The support for the drops 

is not fully understood but is 
thought to be an electrical 
repulsion between the water 
molecules in the drop and those in 
the main body of water. A water 
molecule has a positive side where 
the two hydrogen atoms are 
located and a negative side where 
the oxygen atom is. If the drop's 
bottom surface and the surface of 
the main body of water just 
beneath the drop present the same 
charged side to each other, then 
those two surfaces wili electrically 
repulse each other. Another 
support mechanism is employed if 
the main body of water is 
superheated. In that case the 
evaporation of the bottom surface 

of the drop provides a continuous 
vapor layer to support the drop 
(just as is described in the answer 
to FC 3.65). 

4.122 The soup flow reversal is 
an example of elastic recovery by a 
viscoelastic fluid. When the soup 
has almost come to rest because 

of friction from the sides of the pan, 
the top surface briefly continues to 
move after the lower soup has 
stopped. The surface layer is then 
pulled back by an elastic force 
between it and the lower soup, and 
the swirl is momentarily reversed. 
Oscillations around the equilibrium 
position would continue except that 
the soup is viscous enough to 
damp out the oscillations almost 

4.123 Although this effect, called 
the Kaye effect, depends on the 
elastic nature of the fluid, its cause 
is not well understood. Collyer and 
Fisher suggest that the leap may 
be due to a rapid change in the 
viscosity of the stream as it strikes 
the heap on the main body of fluid. 
The fluids that display the Kaye 
effect are apparently 
shear-thinning ones, that is, their 
viscosity decreases when the fluid 
is sheared (FC 4.126). During its 
fall the stream is un sheared and 
has a relatively high viscosity. 
Upon striking the heap, however, 
the rapid changes in velocity will 
create large shearing in the fluid, 
thereby reducing its viscosity. 
Being elastic also, the stream then 
reflects from the heap. 

4.124 As the viscoelastic fluid 
rotates, the shearing of its layers 
creates stresses that act around 
the circumference of the circular 
path of the fluid, tending to contract 
the fluid to the center of rotation. 
These stresses are not created in 

normal (Newtonian) fluids. Their 
result in this demonstration is to 
push the fluid to the center of 
rotation and up the rod. 

4.125 The compression on the 
falling stream causes the stream to 
buckle. Since the stream cannot 
break under these conditions, the 
buckling makes the bottom of the 
stream circle around as more fluid 
falls than can be absorbed into the 
main body of the fluid. 

4.126 A fundamental explanation 
of how the viscosity of a fluid is 
decreased when the fluid is under 
shearing stress is not currently 
available. Most suggestions 
involve a change in the molecular 
configuration because of the 
shearing. For example, the long 
molecules may be stretched along 
the flow lines created by the 
shearing. As a result, the viscosity 
is decreased. Once the shearing is 
removed, the molecules regain 
their previous orientations, and the 
viscosity increases. 

4.127 The internal stresses in 
the viscoelastic fluid are relieved 
when the fluid emerges, thereby 
forcing the expansion at the tube's 
mouth. One model of this relief and 
consequent expansion considers 
the molecules as being stretched 
when forced through the tube. 
When they emerge they contract 
and consequently swell the fluid. 

4.128 and 4.129 Both of these 
demonstrations are examples of 
elastic recovery by a fluid. The 
silicone putty is highly viscous, but 
the viscosity is lower for slow 
shearing rates. At high shearing 
rates it fractures. 

4.130 The viscosity of quicksand 
increases with shearing, so trying 
to pull yourself out of the stuff 

Answers 265 

quickly is impossible; the more you 
shear the quicksand, the more it 
will hold to you. Move slowly so as 
to keep the viscosity as low as 
possible. The eyes of trapped 
animals may bulge because of the 
large hydrostatic pressure on the 
lower part of the body due to the 
density of the quicksand. (A 
sand-water mixture is denser than 
just water.) 

4.131 If the cylinder is rotated 
slowly, then the dye is pulled along 
a thin layer and spiraled inward 
with each turn. Provided the 
reversal is made before molecular 
diffusion (thermal motion of the 
molecules) can smear the dye, the 
spiral is unwound almost exactly 
by rotating the cylinder back an 
equal number of turns. 

5.1 In order for there to be a clear 
image on your retina, the eye must 
refract the light rays. About two 
thirds of the refraction occurs at the 
surface of the eye. If water is on 
the eye, nearly ail of that refraction 
is lost because the refractive index 
of the eye material is 
approximately the same as that of 
water. If you wear goggles, there is 
a layer of air in front of the eyes to 
give you normal refraction. The fish 
that sees in both water and air 
simultaneously has two retinas and 
an egg-shaped eye lens. In order 
to compensate for the reduced 
refraction for the submerged 
portion of the eye, the eye lens has 
more curvature for the rays coming 
from the underwater scenes. 

5.2 The man would be invisible if 
his index of refraction matched the 
air's index, which is slightly greater 
than exactly 1, the index of 
refraction for vacuum. A greater 
index would result in some 
refraction of the rays coming from 

scenes behind the man, thus 
making his presence noticeable by 
the distortion of the images, 
especially when he walked. In 
order for the man to see, he has to 
absorb some of the incident light. 
Such absorption would have to be 
slight enough that the man does 
not appear as a shadowy figure. In 
short, his index of refraction would 
have to have a real part that is 
approximately equal to 1.0 and an 
imaginary part that is great enough 
that he would absorb enough light 
to see but not so much that the 
subtraction of the light would be 

5.3 Water rises along the side of 
the pencil by capillary action, 
curving the water surface next to 
the pencil. The curved surface 
refracts light into what would 
otherwise have been a shadow 
region of the pencil to give the 
white gap. 

5.4 The coin's image is first 
visible on the water's top surface 
because the rays from the coin are 
reflected from the back surface of 
the container, directed to the top, 
and then are refracted out to be 
seen. If you put your wet hand on 
the back, you destroy that initial 
reflection there. A dry hand has 
much less effect because it has 
relatively few contact points with 
the glass. A wet hand fills the 
spaces between the contact points 
with water. Since the indices of 
water and glass are about the 
same, this filling of the spaces 
effectively increases the contact 
area of the hand with the container 
to about 100%. Much of the light 
rays from the coin that fall on this 
area are therefore absorbed and 
lost. As a result the image on the 
top surface disappears. 

5.5 Light rays from the 
submerged object are refracted at 

the water-air surface, bending 
toward the surface as they emerge 
and, as a result, appear to 
originate from a place higher than 
the true position of the submerged 
object. For normal viewing (eyes 
on a horizontal line) the horizontal 
distance is not distorted. If you turn 
your head so that your eyes are 
along a vertical line, then the rays 
reaching one eye have been 
refracted at a different angle to the 
water surface than the rays 
reaching the other eye. As you 
mentally extrapolate the rays back 
to find the apparent position of the 
submerged object, you place it not 
only higher than its true depth but 
also closer. 

5.6 Rays passing the first plane 
of glass will be partially reflected 
from the inside surface of the 
second plane. Normally this partial 
reflection is insignificant because 
most of the light continues through 
the second pane to be seen. 
However, if the external air 
pressure differs from the air 
pressure between the two panes, 
then the panes are not parallel, 
and part of the internally reflected 
light can produce a faint but 
noticeable ghost image, Consider 
a ray from an object outdoors 
entering the first pane initially 
horizontally. Most of that light goes 
through the second pane and 
enters the room. If this is the only 
light seen, it gives an undistorted 
image of the object. However, part 
of the light is reflected by the inside 
of the second pane, returned to the 
first pane, reflected again, returned 
to the second pane, and finally 
transmitted into the room to 
provide a second, fainter image. If 
the two panes are not parallel, this 

266 Flying circus of physics with answers 

second image is displaced from 
the true image. 

5.7 through 5.11 Ail of these 

problems (except for the story 
about the bird in FC 5.9) are 
examples of mirages and depend 
on the variations with height in the 
refractive index of the air near the 
earth's surface. That index 
depends primarily on the 
temperature of the air. Looming 
(which is an example of what is 
called a superior mirage) can occur 
when the air temperature 
increases with height. The 
observed light rays have originated 
from a distant object, say a 
mountain, at an upward angle to 
the horizon. They are then 
refracted enough by the increase 
in refractive index (due to the 
temperature increase with height) 
that they are bent over for you to 
see. An observer mentally 
extrapolates straight back along 
the observed rays and places the 
image above where the object 
really is. In other words, the image 
looms above the object and is an 
example of a "superior" mirage. 

The oasis mirage is an "inferior" 
mirage in that the image is below 
the true position of the object. In 
that case the object is the sky. 
Light rays from the blue sky are 
refracted by the ground layer of air 
in which the temperature 
decreases with height The rays 
are bent up to the observer, who 
then mentally extrapolates straight 
back along the rays to believe that 
there is a body of blue water on the 
ground somewhere ahead. The 
shimmering due to variations in the 
refraction by the hot air gives the 
illusion of flowing water. The 
pelican could not have seen such a 
mirage because the light rays from 
the sky could never be so refracted 

as to return at such a large angle to 
the ground. 

The Fata Morgana is a more 
complicated mirage in that the 
temperature profile producing it 
does not change linearly with 
height. The temperature increases 
with height but at some 
intermediate height the rate at 
which it increases is less. Such a 
temperature profile, but with a 
more noticeable drop -off at the 
intermediate height, can result in a 
three-image mirage. 

5.12 Most one-way mirrors 
depend on one side (say the room 
in which a criminal is being 
questioned) being more brightly lit 
than the other side (where a viewer 
is). Some of the light incident on 
the glass from the eriminars side is 
reflected by the front and back 
surfaces of the glass. If the other 
side is relatively dark, then the 
criminal sees only the reflected 
light and thinks the glass is a 
mirror. The viewer, on the other 
hand, receives ample light 
transmitted through the glass and 
can clearly see the criminal. The 
mirror effect is enhanced if the 
viewer's side of the glass is coated 
with a very thin layer of metal that 
would increase the amount of 
reflected light to the criminal but 
still allow enough light for the 

5.13 Even though the moon is in 
the earth's shadow, sunlight can 
still illuminate it if the sunlight is 
refracted into the shadow area by 
passing through the earth's 
atmosphere on the edges of the 
earth. However, such refraction 
removes the blue end of the visible 
spectrum for the same reason that 
the sky is blue (FC 5.59) and 
leaves only the red end of the 

spectrum. Hence, the sunlight that 
is refracted sufficiently to illuminate 
the moon is red. The same color 
subtraction is responsible for the 
red skies during sunrises and 
sunsets (FC 5.58). 

5.14 Although mirages are 
normally due to refraction of light 
(see FC 5.7), this particular illusion 
appears to have been a mirage 
due to reflection. The girl probably 
saw a refiection of herself on the 
thin mist. Nothing more than this 
suggested cause has been 
published on reflection mirages 
and their physical possibility can 
only be guessed at now. 

5.15 There is no one equation 
giving the number of images 
possible in the two mirrors as a 
function of the angle between the 
mirrors and the angular location of 
the object with respect to the 
mirrors. The most complete work 
done on the problem is that by 
Chai (989). 

5.16 The green flash is due to 
the separation of the colors in the 
sunlight by the earth's atmosphere, 
similar to the dispersion of light by 
a prism. As a ray from the sun 
enters the earth's atmosphere, it is 
refracted such that it is slightly 
closer to being vertical than before. 
As a result, the sun appears to be 
somewhat higher in the sky than it 
really is. The shorter wavelengths 
of light (the blue end of the 
spectrum) are refracted more than 
the longer wavelengths (the red 
end), and, as a result, there should 
be a blue image of the sun slightly 
higher than a red image, with 
images of intermediate colors 
somewhere in between. However, 
the blue is lost by atmospheric 
scattering (see FC 5.59) and the 
highest image is the next color, 

Answers 267 

green. As a result, green is the last 
color seen just as the image of the 
sun dips below the horizon, 

5.17 The unmixed sugar creates 
a variation In the refractive index 
with depth with the maximum being 
at the bottom where there is more 
sugar. As the laser beam enters 
this solution, let us say initially at a 
slight downward tilt, the beam is 
continuously refracted to a greater 
tilt as it encounters progressively 
greater values of the refractive 
index. Eventually it reflects from 
the bottom surface. As it moves 
upward it again encounters a 
continuously changing refractive 
index and again is continuously 
refracted. This same type of 
refraction, but with sound instead 
of light, is discussed in the answers 
toFC 1.29 and 1.38. 

5.18 The light rays from the sun 
are refracted by the atmosphere. 
The closer the sun is to the 
horizon, the more this refraction is. 
Consider the sun when its lower 
edge appears to be on the horizon. 
Were it not for the refraction, the 
sun would just then actually have 
its lower edge a little more than 
half a degree below the horizon. 
The upper edge, in the meantime, 
appears to be slightly less than 
half a degree from where it would 
be if there were no refraction. As a 
result, the vertical width of the sun 
appears to be somewhat less than 
it would be with the sun overhead 
(actually about 6 arc minutes 
short). The horizontal width suffers 
very little shortening due to 
refraction (about half an arc 
second). Thus, when the sun is on 
the horizon it appears to be an 
ellipse. (Please don't confuse this 
refraction effect with the optical 
illusion of FC 5.134.) 

5.19 The blue ribbon is due to 
the reflection of the blue sky by the 
waves on the horizon. According to 
the answer to FC 5.20, the average 
contribution to the reflected light by 
the horizon waves comes from the 
sky about 30° up from the horizon. 
During much of the day that portion 
of the sky is a deeper blue than the 
rest of the sky, and therefore the 
ribbon should be a deeper blue. 
The reflection polarizes the light 
parallel to the water (see FC 5,49), 

5.20 Certainly the waves do not 
all have a si ope of 1 5°, but the 
average contribution of the light 
scattered by the waves on the 
horizon comes from the sky about 
30° up from the horizon. So, the 
overall effect is the same as if all 
waves did have 1 5° slopes. Waves 
with small slopes are more 
probable than waves with larger 
slopes, but they reflect only a small 
part of the sky. Waves with 
somewhat larger slopes are less 
probable, but they reflect larger 
portions of the sky at greater 
angles to the horizon. Waves with 
relatively large slopes are so 
improbable that they contribute 
almost nothing. The overall effect 
is that the part of the sky at 30° 
from the horizon is most strongly 
reflected by the waves on the 
horizon and that portions of the sky 
at smaller angles have much less 
reflection and are not seen. 

5.21 The tilt of the random waves 
on the water spreads the reflected 
image of the light source (sun, 
moon, or artificial light). The 
spread to the left and right is less 
than the spread between the 
observer and the horizon because 
of the geometry involved in 
reflecting light to the observer. The 
ratio of the width to the length of 

the bright area is sin 8 where is 

the angle of elevation of the light 
source. The dark triangle above 
the horizon is a contrast effect. By 
blocking off the luminous area from 
your field of view, you eliminate 
that illusion, 

5.22 The cloth can glisten if it has 
a regular pattern of threads 
running parallel to each other to 
give a furrowed surface. When 
such a cloth is viewed at certain 
angles, the reflection of incident 
light is relatively large. At other 
angles, the reflection is less. So, if 
the cloth is moved around in the 
light, sometimes it reflects well, 
sometimes not. In other words, it 
glistens. The orientation giving the 
most reflection is when a line 
perpendicular to the furrows 
bisects the angle between the 
incident light ray and the light ray 
reflected to the observer's eyes. 

5.23 The eye produces a real 
image of the nail on the retina that 
is inverted from the nail's 
orientation. The nail looks right 
side up, however, because the 
brain effectively inverts the real 
image in its interpretation of the 
scene. The nail also puts a shadow 
on the retina whose orientation is 
the same as the nail. But since the 
brain inverts the scene on the 
retina, that shadow appears to be 
upside down. 

5.24 The opti mum h ole radius is 
approxiately V' 0.6 kf where X is 
the wavelength of the light and f is 
the distance from the hole to the 
screen or film. Larger holes give 
less resolution in the photograph. 
Smaller holes produce diffraction 
patterns. (Diffraction is an 
interference effect due to the wave 
nature of light. Similar diffraction, 
but with sound instead of light, is in 

268 Flying circus of physics with answers 

FC 1.42 and 1.43.) The pinhole 
camera does suffer chromatic 
aberration because the optimum 

distance to the film for a given 
pinhoie depends inversely on the 
wavelength of light, which varies 
from about 0.40 microns (blue) to 
0.65 microns (red). 

5.25 The images are pinhole 
images made by the tiny holes in 
the leaves. They are always 
present during the day but are 
usually lost in the overall glare of 
light. During an edipse that glare is 
reduced somewhat. 

5.26 Light falling on the dew 
drops is strongly reflected back 
along the path to the sun, that is, 
retroreflected. Part of the reflection 
is at the front surface of the drop; 
part is at the back surface at the 
point on the axis through your eyes 
and the sun. Light incident at other 
angles on the drops can also enter 
the drop to reflect on the backside. 

5.27 Reflectors that return the 
light to its source, even if the light 

source is not on the reflectors 
central axis, are called 
r etr or ef lectors. They can be 
spheres (FC 5.26), triangular 
prisms, or incorporate mirrors and 
lenses, A perfect retroref lector 
would be practically useless since 
the eye is rarely exactly at the light 
source. But most retroref! ectors 
are sufficiently imperfect that the 
cone of light returned toward the 
source is wider than the cone of 
light intercepted by the reflector. A 
simple retro reflector is a corner of 
three mutually perpendicular 
mirrors. A light ray entering the 
corner from any direction will 
reflect off all three mirrors in 
succession and then be returned 
opposite its initial direction. 

5.28 The drops focus the light, 
placing an image of the sun on the 
leaves, which burns the leaves. 

5.29 Chance orientations of the 

water waves reflect light to your 
eyes. The illusion that there are 
streaks of light radiating from the 
head of your shadow is due to the 
required wave orientation for the 
reflection to reach you and the 
constantly changing wave pattern. 

5.30 Cats and other animals 
have retroreflecting eyes that are 
noticeable in otherwise dark 
surroundings. The eye 
incorporates a lens and a curved 
mirror that returns the tight in a 
cone which then passes the source 
of light. In the case of carnivores, 
there is a layer of zinc cysteine 
crystals behind the retina that 
provides the high reflectance. 

5.31 The horizontal line marks 

the height at which falling snow 
melts. The snow reflects more light 
above the line than the water drops 
do below the line. 

5.32 Light does emerge in a 
large range of angles from a water 
drop, but the most intense light 
emerges at the rainbow angles (in 
ray theory you can say that there is 
the densest clustering of the 
emerging rays at the angle). 
Since the different visible 
wavelengths suffer different 
amounts of refraction (blue is 
refracted more than red), the exact 
angle at which the emerging light is 
brightest is slightly different for 
each color. Hence, at the rainbow 
angle the colors are not only bright 
but also slightly separated so that 
they can be distinguished. (Also 
see the answer to FC 5.44.) 
However, the dispersion 
separating the colors is not 

prismatic. The first clue to its true 
nature is in the formation of the 
supernumeraries (FC 5.34). 

The color sequence in the 
secondary bow (which is higher in 
the sky than the primary bow and 
somewhat rarer) is reversed 
because the participating light rays 
reflect twice inside the drop. As a 
result, they emerge at a different 
angle than the rays participating in 
the primary rainbow. Since the 
blue is refracted more than the red, 
the drops contributing the blue to 
the secondary rainbow must be at 
a slightly greater angular elevation 
than the drops contributing the red. 
The exact opposite is true for the 
primary rainbow because only one 
reflection is involved there. Thus, 
the color sequence is reversed. 

More than two rainbows have 
been seen in the lab. [For 
example, see my paper in the 
Amer. J. Physics, 44, 421 
(1976).] A few people have 
reported seeing the third order 
rainbow (corresponding to three 
internal reflections) when the sun 
is low and below some dark 
clouds. In general the higher order 
rainbows are not seen because 
they are dimmer than the glare 
reflected from the surface of the 
drops, the glare transmitted 
through the drop with no internal 
reflections, or the background sky 

5.33 The uneven distribution of 
the red is due to the vertical 
flattening of the falling drops by the 
air flow around them. Since the 
horizontal cross sections of the 
drops remain circular, the colors on 
the vertical legs are the expected 
rainbow colors because the light 
traverses the drops through such a 
circular cross section. On the top of 
the arc the light must go through a 

Answers 269 

flattened cross section, which 
displaces the red inward and 
downward in one's view of the 
bow. As a result the contribution of 
red is diminished. Smaller drops 
are less affected by the air flow and 
therefore can contribute to all parts 
of the rainbow. 

5.34 A correct calculation of the 
rainbow intensities and color 
distribution abandons the 
technique of tracing light rays 
through the drops in favor of 
treating the fight as a wave. Even if 
the incident light wave is a plane 
wave, the emerging light wave is 
not. As a result the emerging light 
creates an interference pattern. 
The major peaks (the brightest 
areas) in the pattern are just the 
bright colors in the usual rainbow, 
so nothing substantial has been 
changed from the previous ray 
approach. Some subtle effects are 
noticed, however. The actual 
angular locations of the colors are 
now more accurate. The change in 
colors with change in drop size is 
finally accounted for(FC 5.44). But 
more important, the interference of 
the emerging waves explains the 
occasional faint bows just below 
the primary bow and just above the 
secondary bow. These extra bows 
are the other peaks in the 
interference pattern. They are 
seen less often only because they 
are less intense than the major 
peaks in the pattern and because 
their visibility depends on 
uniformity of drop size. 

5.35 From all of the sky in the 
direction of the rainbows there is 
the general background sky 
brightness and some glare from 
the reflection of sunlight from the 
outside surface of the drops. Below 
the primary rainbow there is also 

light reflected once inside the 

drops. The brightest of this light is 
at the primary rainbow angle, but 
other such singly reflected light can 
exit any drops at a lower angle in 
the sky than the primary bow. 
However, such singly reflected 
light cannot exit from drops at a 
greater angle than the primary 
bow. A similar but reversed case 
holds for the light reflected twice 
inside the drop. The brightest of 
this twice reflected light exits at the 
angle of the secondary rainbow. 
Other twice reflected light can exit 
from drops at greater angles in the 
sky, but none can exit from drops 
at lesser angles. So, in addition to 
the background light and glare, 
there is an additional light below 
the primary bow and above the 
secondary bow but not between 
the bows. That band between the 
bows is therefore relatively dark. 

5.36 The rainbow is polarized 

parallel to the bow at any given 
point because of the refraction and 
reflection of the light by the water 

5.37 The lunar rainbows are rare 
not only because moonlight is 
much weaker than sunlight, but 
also because of the weather and 
the time the moon is in the proper 
position and condition for making a 
rainbow. The time of day with the 
highest frequency of 
thundershowers is late afternoon 
and early evening (FC 3.41). Thus 
the moon has less opportunity of 
making rainbows. Also, the 
intensity of the moonlight changes 
as the moon changes phase, 
making the chances of a rainbow 
even slimmer. 

5.38 The drops contributing to 

the rainbows are not at any 
particular distance from the 

observer. Only their angle from the 
tine extending from the sun and 
through the observer matters. The 
drops can be anywhere from a few 
yards to several miles distant from 
the observer. If the only drops 
participating are just a few yards 
away, such as with a nearby 
garden sprinkler, then each eye 
sees its own rainbow displaced 
from the other. 

5.39 The rainbow pillar is a leg of 
the primary reflection rainbow. The 
normal primary bow is formed from 
the direct sunlight Near a body of 
water light reflected from the water 
can form another rainbow in the 
sky. Although the geometry 
required for such a reflection 
rainbow is necessarily the same as 
for the normal rainbow, its 
orientation in the sky is different 
from the normal rainbow because 
of the reflection. Were the whole 
reflection rainbow visible, it would 
have its center higher in the sky. 
Thus, near the horizon its leg is at 
a steeper angle to the ground than 
the leg of the normal rainbow. 
Some intensity of the sunlight is 
lost on reflection from the body of 
water, so the reflection rainbow is 
weaker and rarer than the normal 

5.40 In contrast to the preceding 
phenomenon, the reflected 
rainbows are merely the mirror 
images of the normal rainbows. 
Although Minnaert (954) describes 
the two arcs as being identical, 
Humphreys (164) correctly shows 
that the reflected bow appears 
flatter because less of the arc is 
seen than for the normal rainbow 
above it. The difference in 
appearance stems from the 
requirement of scattering angles if 
light emerging from water drops is 

270 Flying circus of physics with answers 

to contribute a rainbow that then 

reflects from the water surface to 
your eyes. The water drops 
meeting such angle requirements 
are at a lower angular elevation in 
the sky than those giving the direct 

5.41 The normal dew bow is just 
a rainbow from the water drops on 
the grass. The primary rainbow is 
roughly 42° from an axis running 
through the sun and the observer's 
eyes (FC 5.32) and would be a 
complete circle if the ground did 
not interfere with the suspension of 
water drops in the field of view. If 
the ground is covered with water 
drops, however, then the part of 
the rainbow below the horizon can 
be seen. The angle of 42° still 
holds, but because the drops are 
limited to a horizontal plane rather 
than filling all of the space in front 
of the viewer, the shape appears to 
be hyperbolic. In the normal 
dewbow the incident light is 
essentially parallel rays from the 
sun. The street light gives 
diverging rays, and although the 
angle of about 42° is still required 
for the bow, the position of the 
drops contributing to the bow takes 
on the initially strange shape 
because of the diverging range of 
incident light rays available. 

5.42 The sun dogs are due to the 

refraction of light by falling 
hexagonal ice crystals that have 
their central axis (which is parallel 
to the six faces) vertical. Although 
the crystals refract light into a large 
range of angles, the brightest of 
the emerging light is at the angle 
that least deviates the sunlight 
from its original direction. That 
angle of least deviation is about 
22° if the sun, the ice crystal, and 
the observer are all in a horizontal 

plane. The observer then sees the 
bright light from the crystals 22° to 
each side of the sun. As the sun 
rises, however, the crystal's axis is 
no longer perpendicular to the light 
rays and the angle between the 
sun dogs and the sun increases 
somewhat. Eventually the sun is so 
high that the brightness is 
eliminated. The sun dogs are 
colorful because the ice separates 
the colors in the same way as does 
a prism. 

5.43 The 22° halo is produced by 

the same type of refraction from 
falling ice crystals as in FC 5.42 
except that the central axes of the 
contributing crystals are randomly 
oriented in a plane perpendicular 
to a ray of incident sunlight. Thus, 
at any point 22° from the sun there 
are some crystals that happen to 
be oriented properly to give bright 
light. The collection of these 
contributing crystals forms the 
halo. Colors are again due to a 
prismlike separation of the colors. 
Since blue is refracted the most of 
the visible colors, it is on the 
outside of the halo. 

5.44 An explanation of rainbows 
involving just the ray theory and 

prismatic separation of colors (FC 
5.32) cannot account for white 
rainbows. The interference theory 
of rainbows used in FC 5.34 is 
needed. The colors in the normal 
rainbow are the major peaks in the 
interference of the light emerging 
from the water drops at the 
rainbow angles. As drops smaller 
than a millimeter in diameter are 
considered, the widths of those 
peaks increase and eventually 
overlap sufficiently to eliminate any 
distinguishable colors. The fight 
exiting at the rainbow angle is still 
relatively bright but now has no 

color and thus gives a white 

5.45 Reflection from the outside 
surfaces of falling hexagonal ice 
crystals give the pillars of light 
above and below the sun. The 
crystals can be short along their 
central axis as compared to their 
width, in which case they are called 
plates. Or they can be longer than 
their width, in which case they are 
called needles or pencils. Both can 
give sun pillars. For example 
consider the plates. The airflow 
around them forces them to be 
horizontal to maximize their air 
drag. If the plates are higher in an 
observer's field of view than is the 
sun, sunlight reflects from the 
bottom of the plates and gives the 
observer a relatively bright area in 
that portion of the sky above the 
sun. If the plates are lower in the 
field of view, reflection is off the top 

5.46 Recent work by Greenler 
(1034, 1065) provides computer 
simulations of the 22° halo and the 
sun pillar. To untangle all of the 
observed and conjectured arcs, a 
complete simulation of light 
scattered from falling ice 
crystals— both plates and pencils 
(FC 5.45), and both oriented and 
spinning — is needed for the whole 
sky and for all positions of the sun. 
Some of the present, although 
perhaps controversial and 
erroneous, explanations for a few 
arcs and halos are the following 
(the letters refer to Figure 5.46): 

(a) and (b) 22° halo and its sun 
dogs: See FC 5,43. 
(c) 46° halo: the refraction of light 
to make this halo is similar to that 
in the 22 c halo with one exception. 
The ray passes through a 90° 
corner, rather than a 60° corner as 

Answers 271 

with the smaller halo, by passing 
through one of the end faces and 
one of the six side faces of the 
crystal. Again, the brightest light is 
with the geometry giving least 
deviation to the rays. The light so 
scattered by appropriately oriented 
ice crystals gives the 46° halo. 

(d) Circumzenith halo: sunlight 
enters and exits through two 
adjacent faces that are 
perpendicular to each other. To 
create the halo, the sun must be 
lower than 32° from the horizon. 

(e) Parhelic circle: light is 
reflected from the vertical sides of 
the falling crystals. 

(f) Sun dogs to the 46° halo: 
these very rare bright patches are 
due to the same scattering as the 
46 c halo but are limited to those 
crystals having their central axis 

(J) Lowitz arcs: to produce these 
arcs, hexagonal ice crystal plates 
must spin about an axis that lies in 
the plane of the plate. Light 
entering one of the hexagonal 
sides then exits through another. 
The maximum brightness of this 
refracted light is for the geometry 
least deviating the incident ray, 
and the arc is the light from a 
collection of the crystals meeting 
this requirement 

5,47 Crown flash is due to the 
mirrorlike reflection of light from 
falling hexagonal ice crystal plates. 
(They are also responsible for the 
sun pillars in FC 5.45.) The electric 
field in the thundercloud makes 
electric dipoles of these crystal 
plates (i.e., makes one side 
positive and the other negative) 
and the dipoles align themselves in 
the field. Normally the plates fall 
with their broad side down so as to 
maximize the air resistance. But 
the electric field of a lightning 

stroke momentarily changes this 
orientation and hence the relative 
brightness from a particular part of 
the cloud. If the change in electric 
field propagates through the cloud, 
then the brightness could also. 

5.48 One of the first suggestions 
was to cover the headlights with 
polarized filters oriented 90° to the 
polarizing filters placed over the 
windshield. With this orientation 
the driver would not see the light 
from an approaching car because 
the polarized light from its 
headlights would not pass the filter 
in front of him. Such a situation 
would also be dangerous. 
Orientations somewhat different 
from the 90° would be better so 
that some of the oncoming 
headlight could be seen. One of 
the drawbacks to the scheme 
(perhaps a fatal one) is that the 
filters also absorb some of tine light 
from the surroundings, as for 
example, the light from a 
streetlight. So the overall view 
would be darker. Another 
drawback is that the tilt of the 
windshield would matter and thus 
would have to be standardized. 

5-49 Direct sunlight is 
unpolarized, that is, the oscillations 
of its electric field are 
perpendicular to the direction of 
travel but along no particular axis. 
The reflection of sunlight from a 
surface will polarize the reflected 
light parallel to the surface, that is, 
the electric field oscillations are still 
perpendicular to the direction of 
travel but are preferentially 
oriented parallel to the surface. 
The extent of this polarization 
depends on the material and the 
incident angle of the light. If you 
are driving toward an afternoon 
sun, for example, the light reflected 

from the road is strongly polarized 
parallel to the road. Polarized 
sunglasses reduce this glare by 
blocking that sense of polarization 
and passing light with vertical 
polarization. On a microscopic 
scale, this blocking means that the 
long molecules in the filters are 
oriented horizontally and will 
absorb light whose polarization 
(and thus electrical oscillations) 
are also horizontal, Much of the 
glare is thus eliminated, but the 
general illumination of the 
surroundings is not as reduced. 

A fisherman can reduce the 
glare of sunlight reflected from the 
top surface of the water and still 
see the light reflected from the fish. 
Of the unpolarized incident light, 
the parallel polarization has been 
preferentially reflected. The light 
entering the water then must be 
preferentially polarized in the 
opposite sense— perpendicular to 
both the direction of travel and to 
the parallel polarization. Once 
reflected from the fish, this light will 
be able to pass through the 
fisherman's sunglasses. Thus, the 
man sees the fish and not the 
surface glare. This explanation is 
not completely correct if the fish is 
more than about 5 ft, deep, 
because thereafter the scattering 
of the light by small particles 
suspended in the water polarizes 
the light horizontally (FC 5.55). 

5.50 The polarization of the 
sunlight scattered by the 
atmospheric particles is derived 
from the same scattering physics 
as in the popular explanation for 
the blueness of the sky (FC 
5.59). The unpolarized incident 
sunlight oscillates the electrons in 
the air molecules (nitrogen, 
oxygen, etc.), which reradiate the 
light. Consider, for example, a sun 

272 Flying circus of physics with answers 

on the horizon and a scattering 
atom directly overhead. Since the 
direct sunlight is unpolarized, the 
electrons in the atom can oscillate 
along any axis in a plane 
perpendicular to the direction of 
travel of the sunlight. You can 
consider such oscillations as being 
either of two cases; where the 
electrons oscillate vertically or 
where they oscillate horizontally as 
you would view this overhead 
atom The vertical oscillations do 
not radiate light vertically so you do 
not see that contribution. Instead 
you see only the light radiated by 
the horizontal oscillations. Such 
light is polarized along the same 
sense as the electron oscillations: 
north-south if the sun is due west. 
In other words, the light scattered 
from that part of the sky is 
polarzed. Similar considerations 
can be made for the rest of the sky 
and for any elevation of the sun. 
Clouds are not polarized because 
of the multiple scattering of the 
light traversing them. Multiple 
scattering is also the cause of the 
neutral points in the sky's 
polarization pattern. 

5.51 The ice is double refracting, 
that is, a beam entering the ice is 
split into two beams each 
experiencing different indices of 
refraction and having 
perpendicular senses of 
polanzation. Instead of the 
arrangement in the problem, first 
consider ice between two 
polarizing filters. Light passing the 
first filter enters the ice, is split into 
two beams, which then propagate 
through the ice at different effective 
speeds (because of the difference 
in the refractive indices they 
experience). When they emerge, 
the two beams may be in or out of 
phase depending on the 

wavelength of the light, the length 
of the crystal, and the difference of 
the refractive indices. The sense of 
polarization of the emerging beam 
will depend on this phase 
difference. Suppose that when, 
say, the yellow of an initially white 
beam emerges that its sense of 
polarization happens to be 
perpendicular to the second filter's 
polarization sense. The second 
filter will therefore block the yellow 
light, and an observer will see the 
other colors in the visible range in 
the light from that filter. In the 
problem there are no polarizing 
filters, but the sky provides 
polarized light and the reflection of 
the light from the water pool 
provides the second polarizing 

5.52 The cellophane can be 
considered as having two special 
axes. Light polarized along one of 
these axes will experience a 
certain index of refraction. Light 
polarized along the other will 
experience a different index of 
refraction. If the incident light is 
polarized along a direction lying 
between these two special 
cellophane axes, then the light is 
effectively split into the two 
polarization senses of the 
cellophane and propagates 
through the cellophane at different 
effective speeds because of their 
difference in the refractive index. 
Upon emerging, these two 
polarization senses of the light are 
out of phase. The result is that the 
net polarization sense of the lig ht is 
rotated by the cellophane. 
Normally two perpendicular 
polarizing filters wilt not transmit 
light. But with the cellophane 
inserted between them, the 
polarization sense of the light 
passing through the first filter is 

rotated by the cellophane. Then 
part of the light's polarization 
sense happens to lie along the 
polarization axis of the second 
filter, and some of the light gets 
through the second filter. 

The food wrap does not have 
such special axes until it is 
stretched. The stretching 
untangles the spaghetti of the long 
molecules, orients the molecules 
along the direction of stretching, 
and thus makes them polarizing 
filters. Light whose electric field 
oscillates perpendicular to these 
oriented long molecules pass 
through the wrap, whereas the light 
having its electric field parallel to 
the molecules does not pass as 

5.53 The spots indicate the 
stress points in the bonding of the 
glass plates and thus behave like 
the stretched food wrap in the 
preceding problem. 

5.54 The sense of polarization of 
the light entering the syrup is 
rotated by the helical structure of 
the syrup molecules. The rotation 
depends not only on the type of 
syrup but also on the wavelength 
of the light, the blue end of the 
visible range being rotated more 
per unit length of syrup than the 
red end. What colors are seen 
through the second filter depends 
on which of the colors that filter 
happens to block when the light 
emerges from the syrup. For 
example, suppose the second filter 
blocks the sense of polarization 
that yellow light happens to have 
when it emerges from a particular 
container of syrup. Then an 
observer will see not the white of 
the initial light, but the other colors 
in the visible range besides yellow. 

5.55 The polarization detection 

Answers 273 

lies in the ultraviolet detectors of 
the insect eyes. There, the 
rhabdoms, which act as light 
guides in the photoreceptors, are 
twisted: some one way, the others 
the other way. The direction for 
maximum sensitivity of the 
polarization of the incident light 
differs for these two senses of 
twisting by about 40 c . Thus, two 
rhabdoms acting together could 
determine the polarization sense of 
the incident light. That 
determination, along with an 
intensity determination by an 
ultraviolet detector insensitive to 
the polarization, orients the insect 
with respect to the sky. 

5.56 A dichroic crystal can be 

considered as having two 
polarization axes. If the incident 
light is polarized parallel to one of 
these axes, then the crystal is 
clear. If the light happens to be 
polarized parallel to the other axis, 
then the crystal is dark blue. By 
orienting the crystal and observing 
its color, the Vikings could detect 
the polarization of the sky, With 
experience they could infer the 
position of the sun, even if the sun 
was below the horizon. Cloud 
cover, however, destroys the 
polarization of the sky light and 
would make the crystal useless. 

5.57 A blue absorbing pigment in 
the macula lutea (the depression in 
the eye's rear) absorbs according 
to the polarization of the incident 
light. For example, blue vertically 
polarized light is absorbed 
horizontally to leave a horizontal 
yellow hourglass (yellow is blues 
complementary color). 

5.58 and 5.59 The basic color 
determination of the sky is in the 
wavelength dependence of the 

scattering of sunlight by the 
atmospheric molecules according 
to the Rayleigh scattering model. 
The electric field of the incident 
sunlight oscillates the electrons in 
these molecules, which in turn 
radiate light. The overall effect is to 
scatter the sunlight. Light with 
shorter wavelengths (the blue end 
of the visible range) is deviated 
more from its original direction than 
is light with longer wavelengths (the 
red end). When the sun is near the 
horizon the sky above an observer 
is therefore largely blue. The sky 
more than 90° from the sun is less 
blue because it is illuminated with 
sunlight which must traverse a 
long path through the atmosphere 
and is therefore somewhat 
depleted in the blue. The sky near 
the sun on the horizon is red or 
yellow because it too is illuminated 
with light whose long traversal of 
the atmosphere depletes the blue. 
Dust from a variety of sources 
(e.g., volcanos, forest fires) can not 
only scatter additional tight, but can 
also display a different wavelength 
dependence than the Rayleigh 
scattering. Sunsets and sunrises 
after a major volcanic eruption can 
be brilliant (and also lead to the 
blue sun and moon of FC 
5.84), The particular hues seen in 
any particular sunset are due to a 
combination of the normal 
Rayleigh scattering and the dust 

5.60 The purple light is due to 
dust at an altitude of about 20 km 
in the atmosphere. Some of the 
sunlight passes through a layer of 
the dust, comes out underneath 
the layer, and then because the 
layer is curved around a spherical 
earth, reenters the layer. Its first 
passage through the layer scatters 
out most of the short wavelength 

(blue and green) light, so the light 
reentering the layer is red. Some of 
this reentering light is then 
scattered by the dust to an 
observer. That observer also 
receives blue light from sunlight 
scattered by the atmosphere 
above the dust layer. (In other 
words, the blue light of FC 5.59.) 
The combination of red light due to 
the dust and the normal blue light 
gives an overall purple for the 
observer. The second purple light 
is believed to be due to a second 
dust layer at an altitude of 70 to 90 

5.61 The enhanced zenith 
blueness comes as a surprise. 
According to the Rayleigh 
scattering of FC 5.59, the zenith 
sky should be blue-green and then 
yellow as the sun sets. The 
missing element in a simple 
Rayleigh scattering picture is the 
absorption by the atmospheric 
ozone in the red end of the visible 
spectrum. With the red end 
removed, the blue end is left and 
appears richer. The geometry 
favoring such a blue enhancement 
occurs when the sun is about 6° 
below the horizon and the light 
scatters from directly overhead the 
observer. The blue is further 
increased by dust in the 
atmosphere because the dust 
absorbs more of the red and yellow 
from the direct sunlight than the 
blue (see FC 5.84). 

5.62 Next to the earth's shadow 
the sky is illuminated with sunlight 
from which all of the short 
wavelength (blues and greens) 
have been subtracted (FC 5,58). 

5.63 The particulate matter 
(industrial pollution, smog) with 
radii smaller than about 0.4 micron 
scatters the blue light out of the 

274 Flying circus of physics with answers 

light reaching the distant observer. 

5.64 The sky is bright because of 
the scattering of sunlight by the air 
molecules. But there is a problem. 
For every molecule scattering light 
to an observer there is, on the 
average, another molecule on the 
line of sight and half a wavelength 
closer to the observer. The light 
scattered from these two 
molecules arrive exactly out of 
phase at the observer and 
therefore cancel each other. Since 
the argument can be repeated for 
any portion of the sky except 
directly toward the sun, the sky 
should be completely dark except 
in that special direction and except 
for the stars and planets. The 
argument has a slight flaw, 
however. Although the molecules 
can be paired this way on the 
average, they cannot be 
continuously paired because of the 
fluctuations in the distribution of 
the molecules, Were there no 
fluctuations, the sky would be dark. 

5.65 Apparently nothing beyond 
a description of the effect has been 
published. The yellow glasses may 
be of advantage if the haze is 
composed of relatively small 
particles, smaller than about 0.4 
micron in radius. Such small 
particles scatter the short 
wavelengths of light (the blue end) 
more than the long wavelengths 
(the red end). Thus the reds and 
yellows may illuminate the ground 
in a more direct beam whereas the 
blues and greens, having suffered 
more scattering in the haze, are 
more diffused. By eliminating the 
blues and greens, an observer 
might be able to see more of a 
shadow of an object in the field of 

5.66 Instead of being easier to 

see, stars are harder to see 
through a shaft. Although most of 
the sky is blocked off, the sky 
surrounding the star's image is still 
just as bright as without the shaft. 
The shaft certainly cannot make 
the star itself brighter. 
Experimental work on viewing a 
small luminous test area in a large 
surrounding dark area indicate that 
the threshold in distinguishing the 
test area is decreased if the 
lumination of the surrounding area 
is increased until it is about the 
same as the test area. Instead of 
being more easily seen, stars are 
therefore harder to see through a 
shaft because their threshold of 
visibility is increased when the sky 
is blocked off. 

5.67 If the water is pure and 
deep, it is blue due to the surface 
reflection of light from the blue sky. 
Shallower water has greater green 
because of reflection from the 
bottom. Contamination can add a 
variety of hues to the water 
because of selective absorption or, 
in the case of micron-size particle 
suspensions, because of the 
scattering of the light. This latter 
effect is similar to the scattering in 
PC 5.87 and 5.88. 

5.68 The greenish tinge is added 
by the reflection from green 

vegetation. A similar upwelling of 
light adding features to an overcast 
sky is responsible for the sky maps 

of FC 5.72. 

5.69 The illumination of the 
"dark" part of the moon (i.e., the 
part of the moon in a shadow from 
the direct sunlight) is due to 
earthshine, the light reflected from 
the earth s atmosphere and 

5.70 The scattering of light off 

objects much smaller than the 
wavelength of visible light follows 
the Rayleigh scattering model in 
FC 5.59. The water drops in the 
clouds are usually larger and 
merely reflect the sunlight from 
their outside surfaces. No color 
separation results from such 
reflection, and the scattered light 
remains white. (An exception is in 
FC 5.73.) Very dense clouds are 
black because little of the sunlight 
is able to penetrate them, being 
either absorbed by the water or 
reflected upward. 

5,71 Sunlight scatters from water 
molecules as from any other 
molecule in the atmosphere, and 
so individual water molecules 
contribute to the sky brightness 
(FC 5.58). The scattering from 
water drops is greater than from an 
equal number of individual 
molecules because of their close 
spacing in the drop where adjacent 
molecules are about 1000 times 
closer than the wavelength of 
visible light. Consider two such 
adjacent molecules. When the 
sunlight oscillates their electrons, 
the oscillations are in phase 
because the electrons sample 
essentially the same part of the 
incident light wave. The electric 
fields radiated by those electrons 
are also in phase and 
constructively add to give twice the 
electric field as from a single atom. 
The intensity of the radiated light is 
the square of the amplitude of the 
radiated electric field and therefore 
must be four times that from a 
single atom. If these two molecules 
are well separated (much more 
than the wavelength of the light), 
there is no average constructive 
interference and the radiated 
intensity is only the sum of the 
intensity from each, that is, only 

Answers 275 

twice the intensity from a single 
atom. The clouds are bright 
because of the constructive 
interference of the closely spaced 
water molecules in the water 

5.72 The maps are formed from 
the selective reflection of sunlight 
from the ice and water surface and 
then from the clouds. For example, 
the direct sunlight is reflected more 
from the solid ice than from the 
water. Since both reflect well, the 
difference in the reflections can be 
seen on the bottom of the clouds. 

5.73 The mother-of-pearl clouds 
are composed of small drops 
whose radii (0.1 to 3.0 microns) are 
near or somewhat larger than the 
wavelength of visible light. Such 
drops scatter light according to the 
Mie model rather than the Rayleigh 
model of FC 5.59 for smaller drops 
or the simple reflection from larger 
drops. The diffraction of the light 
around the drops depends not only 
on the drop radius but also on the 
wavelength of the incident light and 
is therefore responsible for the 
beautiful colors. The clouds can be 
viewed up to two hours after 
sunset because of their high 
altitude: they are still illuminated for 
that long after a ground observer 
has entered twilight. 

5.74 The interference fringes 
result from the scattering of the 
light by the dust particles on the 
front surface of the mirror. 
Consider two rays. One is 
scattered by a dust particle before 
entering the mirror and being 
reflected in the normal way. The 
other is first reflected in the normal 
way and then is scattered by the 
same dust particle on leaving the 
glass. Since the paths taken by 
each were slightly different, the 

rays can have a variety of possible 
phase differences when observed 
together, depending on the angle 
of the rays and the wavelength 
(color) of the light. Thus, the light 
shining on the dusty mirror 
produces an interference pattern 
for the observer, with the colors 
separated because of the 
wavelength dependence in the 
phase difference of interfering 

5.75 The light beam dims not 
only because of the spreading of 
the beam but also because of the 
attenuation of the beam by the 
scattering of the atmosphere. 
(Were there no scattering, the 
beam would be invisible.) The 
attenuation exponentially 
diminishes the beam's intensity, 
giving a rather abrupt end to the 

5.76 Both the zodiacal light and 
the gegenschein are due to the 
scattering of sunlight from 
interplanetary dust, probably 
derived from the astroidal belt. The 
dust giving the zodiacal light lies 
inside the earth's orbit and is 
visible only under the special 
circumstances described in the 
problem. The gegenschein is 
sunlight backs catte red from dust 
outside the earth's orbit 

5.77 The windshield wiper rubs 
circular groves of gummy dirt on 
the windshield that then reflect light 
to the driver. The brightest 
reflection occurs when the incident 
light ray is perpendicular to a 
tangent to the grooves. The 
collection of these brighter 
reflections forms the streak of light 
along a radius of the curve through 
which the wiper moves. 

5.78 The brown is primarily due 

to selective absorption by the 
nitrogen dioxide in the hazes. 

5.79 The glory results from light 
backscattered to its source by 

small particles whose radii are 
near or somewhat larger than the 
wavelength of visible light. The 
scattering is described by the Mie 
theory rather than the Rayleigh 
theory for smaller particles (such 
as in FC 5.59) or by the normal 
reflection and refraction models for 
larger particles. The light that is 
returned in the direction of the light 
source enters a drop on an edge 
and exits from the edge on the 
opposite side of the drop after 
suffering both a reflection within 
the drop and a skimming along the 
drop's surface. That skimming, 
which is described as being a 
surface wave, is not part of the 
standard ray optics used in 
modeling a rainbow (FC 5.32). The 
return angles for different incident 
colors are slightly different and 
thereby produce the distinct 
colored rings around the shadow of 
the observer's head. Since the 
angles involved in a particular 
pattern depend on the size of the 
drops, the colors are lost if the 
drops in the cloud have a large 
range of sizes. 

5.80 The solar and lunar corona 
are the diffraction patterns of the 
light from the small water drops in 
the line of sight. The diffraction is 
handled best with the Mie theory 
as in (FC 5.79) but can be 
approximated with the 
conventional diffraction of light 
around a small sphere (as in FC 
5.96 and 5.98). In the latter 
interpretation, the light rays 
passing opposite sides of a water 
drop interfere with each other on 
the other side of the sphere to 

276 Flying circus of physics with answers 

create bright and dark rings 
corresponding to constructive and 
destructive interference. The 
angular positions of the bright and 
dark rings depend on the drop size 
and the wavelength of the light. If 
the drops are uniform in size, then 
rings of different colors can be 
distinguished, the longer 
wavelengths (red) on the outside 
and the shorter wavelengths (blue) 
on the inside of a ring. 

5.81 The frosty glass corona 
results from the scattering of light 
as in the preceding problem but 
with a few changes. Instead of 
being randomly spaced spheres, 
the drops are now fairly uniformly 
spaced, flat drops. 

5.82 The Bishops Ring is a 
diffraction pattern from small 
particles, usually dust from 
volcanic eruptions, in which 
settling has sorted the suspended 
particles to a uniform size. As in FC 
5.79 the Mie theory of scattering is 
needed to calculate the intensity of 
the scattering pattern for these 
particles whose radii are about the 
wavelength of visible light. 

5.83 Colored rings can be seen 
surrounding street lights even if the 
night is perfectly clear Similar to 
the corona in the previous 
problems, these corona result from 
diffraction of light around small 
objects which are about the 
wavelength of visible light in size. 
The cifference in this corona is that 
the objects are inside the eye. 
Some of the possible diffracting 
objects responsible for these 
entopic halos are the radial fibers 
in the crystalline lens or the mucus 
particles on the corneal surface. 
Similar entopic diffraction patterns 
are in FC 5.96. 

5.84 In contrast to the Rayteigh 
scattering in FC 5.59, the blue 
moons are due to the scattering of 
light by atmospheric aerosols 
whose radii range from 0.4 to 0.9 
micron (which contains the 
wavelength range of visible light). 
Particles in this size range scatter 
the long wavelength end (red) of 
the visible range more than the 
short wavelength end (blue). As a 
result, a normally white moon seen 
through such an aerosol will have 
the red end of the spectrum 
scattered out, leaving the observer 
with the blue end and thus a blue 
moon. These aerosols are 
occasionally produced by volcanic 
eruption or combustion as in large 
forest fires. The selection of this 
size range can result from the 
particles settling in the atmosphere 
or from condensation increasing 
the size of small nuclei until they 
are within this size range. 

5.85 In spite of several studies, 
the value of yellow fog lights is not 
clear. If the particles are smaller 
than about 0.4 micron in radius, the 
blue will be scattered more than 
the red end of the visible spectrum. 
Yellow light would therefore better 
penetrate the fog because it has a 
longer wavelength than blue and 
green. However, for the particular 
size range described in FC 5.84, 
the result could be the exact 
opposite. For even larger particles 
as in a true fog, the yellow would 
be of no advantage. One problem 
in these general conclusions is that 
the absorption of the light by a 
particular type of suspended 
particle could be important. 

5.86 The blue results from the 
scattering of light from very small 
particles, smaller than the 
wavelength of visible light. They 

can be macromolecules (large 
molecules) of terpenes released by 
the vegetation. Or they can be 
particles released from the tips of 
the vegetation (e.g., the tips of a 
leaf) where the electric field is 
relatively high (FC 6,33) and brush 
discharge (FC 6.46) might occur. 
The scattering is adequately 
modeled by Rayleigh scattering 
(FC 5.59) in which the blue is 
scattered more from the direct 
sunlight than are the other colors. If 
the particles are closer to being the 
size of the wavelength of light, then 
the Mie scattering theory is needed 
to predict the exact scattering 
intensities and color. 

5.87 In order for you to see your 
own shadow in the shallow water, 
you must be able to distinguish the 
light reflected from the top surface 
of the water. In clear water that 
relatively feeble light is lost in the 
light reflected from the water's 
bottom. With mud in the way, the 
bottom light is partially or totally 
eliminated, allowing you to 
distinguish the light and dark areas 
from the surface reflection. To see 
the shadows of other people, there 
must be more elimination of the 
bottom light. 

The colorful edges on shadows 
result from the scattering of light by 
small particles suspended in the 
water. They, like the atmospheric 
particles of FC 5.59 and the other 
particles in FC 5.88-5.90, scatter 
the shorter wavelengths (blue). 
Consider viewing a shadow near 
your own shadow. The nearside is 
blue because this particle 
scattering is distinguishable 
against the dark background of the 
shadow. The far side of the 
shadow is red because light from 
that side has had the blue 
component removed by the 

Answers 277 


5.88-5.90 In each of these 

cases, light is scattered from very 
small particles. As in the 
arguments for the blue sky (FC 
5.59), the Rayleigh theory of 
scattering is applicable for particles 
smaller than the wavelength of 
visible light In such cases blue 
light is scattered more than red 
light. Thus, the suspended milk 
globules and the smoke particles 
appear to be blue when seen while 
looking from the light source or 
from the sides, but appear to be 
red or yellow when seen while 
looking toward the light source, (In 
the campfire smoke case, the 
smoke is first seen because of sky 
light coming from behind the 
viewer and then later seen 
because of sky light in front of the 
viewer,) If the particles are near the 
wavelength of visible light or 
somewhat larger, then the Mie 
theory of scattering is needed 
(The Mie theory is used in FC 5.73 
for direct backscatter.) When 
cigarette smoke is inhaled, 
condensation in the mouth 
increases the drop radii such that 
they are comparable to the 
wavelength of light, and yellow is 
preferentially scattered instead of 

5.91 The colors in a soap or oil 
film are due to the same type of 
thin film interference that is 
responsible for the blue Morpho 
wing in FC 5.94. Briefly, light 
reflected from the first surface of 
the film interferes with the light 
reflected from the second surface. 
Whether the interference is 
constructive or destructive 
depends on the wavelength of the 
light, the refractive index of the 
film, and the path length of the light 

inside the film. If the film is less 
than about one fourth the 
wavelength of light and has air on 
both sides, as with a soap film held 
on a vertical wire hoop, the 
interference is destructive and the 
film appears dark to an observer 
on the same side of the film as the 
light source. As one considers 
progressively thicker films, the 
interference gives progressively 
longer wavelength colors for those 
experiencing constructive 
interference in reflection. If a thin 
soap film is held vertically and 
illuminated with white light, the top 
portion may be thin enough to be 
dark. Further down the film are the 
colored bands corresponding to 
the constructive interference. But, 
mysteriously enough, just below 
the dark portion is a white strip. For 
the film thickness there, partially 
constructive interference comes 
from the entire range of visible light 
and therefore gives the observer a 
white light reflection (Bayman and 
Eaton, personal communication), 

5.92 The source of these rings 
have apparently not been 
investigated but they seem likely to 
be the entoptic halos of FC 5.83 
caused by mucus particles or small 
water drops on the surface of the 

5.93 Liquid crystal, which is a 
material somewhere between 
being a liquid and being a solid, 
comes in three basic types, 
depending on its molecular 
arrangement. The smectic type 
has its molecules aligned in the 
same direction and in parallel 
layers. The nematic type has 
similar alignment in a single 
direction but lacks the layering. 
The third type, the cholesteric one, 
is responsible for the colors in the 

liquid crystal toys now being sold in 
the United States. This type 
contains layers of molecules in 
which the molecules of any one 
layer are aligned in the same 
direction parallel to the plane. The 
alignment direction shifts from 
layer to layer such that a vector 
giving the alignment would rotate 
in a helical path as one considered 
deeper and deeper layers. The 
pitch of this helical path determines 
the wavelength of the light strongly 
reflected by the cholesteric liquid 
crystal. Other wavelengths merely 
pass through the crystal. By 
applying pressure to the crystal 
(the toy comes packaged in a 
flexible plastic container) or by 
changing the temperature of the 
crystal, one can alter the pitch 
angle and therefore vary the color 
selectively reflected by the crystal. 

5.94 The rich blue from the top 
surface of a Morpho butterfly wing 
is due to thin film interference of 
light from thin terraces that lie 
almost parallel to the wing and on a 
support structure sprouting almost 
perpendicular to the wing. Of the 
white fight striking such a thin 
terrace, part is reflected (call it ray 
A) and part is transmitted into the 
terrace, Of the latter, part (call it B) 
is reflected from the bottom 
surface of the terrace and emerges 
upward along with A. Rays A and B 
can interfere with each other 
constructively or destructively 
depending on their phase 
difference. That phase difference 
depends on the wavelength of the 
light, the thickness of the terrace, 
the refractive index of the terrace, 
and the angles of the light entering 
and leaving the terrace. For light 
incident perpendicularly to the 
terrace, the wavelength 
corresponding to blue light will 

278 Fly hi 9 circus of physics with answers 

produce emerging rays A and B in 
phase so that they constructively 
interfere, Rays A and B of all of the 
other colors of the incident white 
light more or less destructively 
interfere and do not contribute 
noticeable light to the observer. As 
a result the observer sees blue. As 
the observer changes either the 
angle of view or the angle of 
incident light, the path length of the 
light inside the terrace changes, 
thereby varying the phase 
difference between rays A and B. 
The wavelength giving maximum 
constructive interference changes 
as a result, and a slightly different 
blue hue is seen. 

5.95 The dark lines between 
your fingers are the dark fringes of 
the diffraction of light through the 
space between the fingers. The 
light passing through part of the 
slit, say adjacent to a finger, 
interferes destructively with light 
passing through a different part of 
the slit, say further from that finger, 
to give a dark line at the observer. 

5.96 The eye floaters are the 
diffraction patterns of light passing 
spherical blood cells floating just in 
front of the fovea on the retina. 
(The fovea is a pit of densely 
packed cones directly opposite the 
opening of the eye.) Blood cells 
loosened by old age or violent 
blows to the head swell to spheres 
by osmotic pressure when they 
float in the watery matter in front of 
the retina. 

5.97 If the photograph is 
exposed just right, it might record 
spikes of the stars because of their 
twinkling (FC 5,102). Spikes can 
also be present because of the 
diffraction of the star light by the 
straight sections of the camera's 
aperture- These apertures are not 

perfectly round but are composed 
of many straight edges so that the 
aperture width is adjustable. The 
human pupil is not perfectly round 
either, and diffraction around the 
straight edges creates spiked stars 
there too, The spikes must always 
appear in pairs, 

5.98 The interference rings 
shown in Figure 5.98 are the 

diffraction pattern of the light by the 
sphere. Light passing one side of 
the sphere interferes with light 
passing the other side to give 
bright and dark rings on a distant 
screen. The center of the pattern is 
equidistant from the two sides, and 
the light rays from the two sides 
arrive in phase to give constructive 

5.99 and 5.100 The cause of 

shadow bands is not well 
understood. Probably the best 
current explanation is that they are 
interference patterns of light that 
traverses air cells of varying 
densities. Such cells in the upper 
atmosphere could be naturally 
occurring turbulent cells. 

5.101 The lake acts as a single 
slit, and the observer flies through 
the maxima and minima of its 
diffraction pattern. 

5.102 Stars twinkle because the 
air is turbulent, which ultimately is 
due to uneven heat distributions in 
the atmosphere. Small turbulent 
cells, several centimeters or more 
across, are constantly present to 
refract the passing starlight first 
one way, then another. This small 
shimmy is noticeable with the small 
star images but less noticeable 
with the larger images of the moon 
and the planets. 

5.103 The ultraviolet light is 
absorbed by the organic molecules 

in the pigments and afters their 
molecular bonding, eventually 
eliminating most of the color 
properties of the pigment, This 
ultraviolet fading of colors was 
discovered to be one of the most 
serious threats to paintings hung in 
modern museums that had begun 
to install common fluorescent 
lamps for uniform illumination. The 
lamps also emitted appreciable 
ultraviolet light Now, either the 
lamps or the paintings are filtered 
to remove the ultraviolet light, or 
the museum has returned to 
incandescent bulbs. 

5.104 Light has momentum and 
can therefore exert a force, The 
laser used in this type of 
experiment provides an intense 
beam of light that exerts sufficient 
force on the sphere to raise it The 
stability is due to the refraction of 
light by the sphere. The laser light 
is most Intense in the center of the 
beam. Consider a sphere 
somewhat off center but still in the 
beam. Light entering the sphere 
near the beam's edge refracts into 
the sphere, propagates across the 
sphere, and then refracts out of the 
sphere toward the center of the 
beam. That light beam has 
suffered a net deflection, and 
therefore must exert a force on the 
sphere. Light entering on the side 
near the beam's center suffers 
similar deflection but toward the 
edge of the beam. Both deflections 
provide lift to the sphere. Both also 
provide sideways forces. But the 
light deflected toward the center is 
less intense than the light deflected 
toward the edge. Thus, the net 
sideways force is toward the 
center. If the sphere wanders from 
the center, this net sideways force 
brings it back. 

Answers 279 

5.105 The dark and bright bands 
are the diffraction pattern from the 
screen. You can see similar but 
more colorful patterns by viewing a 
light through an umbrella's fabric. 

5.106 The range over which a 
star radiates light depends on its 
surface temperature (to the fourth 
power when expressed in Kelvin 
degrees). The higher the 
temperature of the star, the lower 
the wavelength at which the peak 
of its radiation occurs, A cool star 
may have an insignificant amount 
of radiation in the visible range. As 
one considers progressively hotter 
stars, the radiation range enters 
the visible range from the red end. 
Thus, a star may have only red or 
red -yellow radiation in the visible if 
its temperature is just right. A 
hotter star could have its peak in 
the center of the visible and then 
emit all the colors approximately 
uniformly. Such a star would be 
white, as is the sun. A still hotter 
star could have its peak in the 
ultraviolet and emit more blue light 
than the other colors in the visible 
and therefore appear somewhat 

5.107 As yet the lights 
associated with tornadoes are not 
explained. In fact, tornadoes 
themselves have not been 
explained (FC 4.68). Most likely 
the light results from the electrical 
discharges present in the 

5.1 08 The light is from molecules 
excited by charge differences on 
the crystal planes as the crystals 
are fractured in the pounding and 
scrapping of the stirring. 

5.109 Solar ultraviolet light is 
responsible for both tanning and 
sunburning. If you are exposed to 

large or lengthy doses of ultraviolet 

light, both the dermis and 
epidermis of the exposed skin may 
be damaged. As a result the 
capillary vessels dilate and bring 
more blood to the skin surface, 
both reddening and warming the 
skin. Shorter exposures to the 
ultraviolet light tans light- colored 
skin by first oxidizing a pigment 
normally without color and then by 
activating (perhaps indirectly by 
deactivating an inhibitor) 
tyrosinase. This activation 
increases the amount of melanin, a 
brown or black pigment. The 
melanin protects the nuclei of skin 
cells by forming a layer over the 
cells which filters out the 

Suntan and antisunburn lotions 
come in three main types. Some 
(with zinc oxide or titanium oxide) 
screen all the ultraviolet and visible 
light and provide no tanning but do 
protect sensitive skin. Others (e.g., 
benzophenones) absorb all of the 
ultraviolet and also provide no 
tanning. The third group 
(containing substances such as 
aminobenzoic acid) provides both 
tanning and protection against 
sunburn by selective absorption. 
The ultraviolet wavelengths extend 
from about 0.28 microns to about 
0.40 microns. Shorter wavelengths 
do not pass through the 
atmosphere, and longer 
wavelengths are in the visible. Of 
this range, the wavelengths 
between 0.29 and 0.32 microns 
are the most efficient in 
sunburning, whereas the 
wavelengths between about 0.31 
and 0.40 microns are the most 
efficient in suntanning. The point of 
the third class of lotions is to filter 
out the wavelengths below about 
0.31 microns. 

Sunburn and tanning are less 

likely in the morning or Jate 
afternoon because the sunlight 
must traverse a greater path 
through the atmosphere and more 
of the ultraviolet light is absorbed. 
Glass also absorbs the ultraviolet 
waveiengths. Sunburn is more 
likely on high mountains because 
of the shorter path length of the 
light through the atmosphere. It is 
more likley at the oeach because 
of the ultraviolet reflections from 
the sand. 

5.110 and 5.111 In each of these 
luminescent cases two materials 
are responsible for the light 
production. These materials are 
given the general names of 
luciferin and luciferase, but what 
they are differs among the 
organisms. The luciferase is just 
an enzyme, a biological catalyst for 
the reactions in the light 
production. Marine creatures can 
be luminescent in three ways. 
They may have cells designed 
specifically for that purpose, 
perhaps even advanced enough to 
resemble lanterns. They might 
instead issue luminescent clouds. 
Or they actually may not be 
luminescent themselves but play 
host to luminescent bacteria. The 
dinoflagel fates turn the sea red, 
yellow, or brown during the day by 
their natural color, but at night they 
glow blue when disturbed. Some 
internal clock regulates that light. 
Dinoflageilates kept under 
continuous dim light still will have 
their maximum light output about 1 
a.m. when disturbed. Such rhythm 
may last for several weeks under 
the dim light. Fireflies set off a 
series of chemical reactions to 
produce light. Their conversion of 
energy to light is 100% efficient in 
that one photon is emitted for each 

280 Flying circus of physics with answers 


luciferin molecule oxidized in the 
chemical reactions. The light is said 
to be ''cold' 1 light because, in 
contrast to incandescent bulbs, 
candle fire, red-hot pokers, and so 
on, the firefly light does not result 
from high temperatures and rapid 
thermal agitation of the molecules. 
Bacterial light, which is responsible 
for much of the luminescence 
reported for food, is a part of the 
natural process of that bacteria in 
obtaining energy from nutrients. 

5.1 1 2 This type of glass contains 
small crystals that react to the 
illumination. For example, if the 
crystals are silver bromide, then 
the fight transforms the silver ions 
to silver atoms that then darken the 
glass. The silver atoms are still 
trapped near the bromide, 
however, so as soon as the light is 
dimmed, the two recombine, and 
the darkening is reversed. 

5.1 13 The black-light poster 
fluoresces by absorbing ultraviolet 
light and then radiating visible light. 
Under an ultraviolet light the poster 
seemingly glows without any 
stimulus. Whiter- than- white soaps 
do almost the same thing. They 
convert the natural ultraviolet to 
blue light and thus add to the 
visible light radiated by the 
materials containing the soap 
product. In the advertising jargon, 
the resulting "white" (meaning 
visible) light is more than the 
natural visible light. 

5-114 Electrons emitted by an 
electrode collide with an atom of 
mercury vapor, exciting one of the 
outer electrons in the atom. That 
excited atom quickly deexcites to 
return the electron to its former 
energy level. As a result of the 
deexcitation, the atom emits 
ultraviolet light that is absorbed by 

phosphor crystals coating the 
inside of the tube. The deexcitation 
of the crystals results in the visible 
light we see. The crystals should 
emit some light for at least two 
cycles of the 1 20 cycles a second 
at which the maximum discharge 
occurs (the rates can differ with the 
country). If the crystals deexcited 
instantaneously after being 
excited, then the tube would have 
an intolerable flashing. 

5.115 The speckle is an 
interference pattern of incident 
parallel rays (spatially coherent 
light) scattering from the very small 
structures on the diffuse scatterer. 
Spatially coherent means that the 
phase of the fight emitted by one 
portion of the light source is 
correlated with the phase of the 
light emitted by another portion. 
Such a correlation is needed to 
maintain a stationary interference 
pattern. To some extent direct 
sunlight is spatially coherent and 
can produce these speckle 
patterns. The apparent motion of 
the pattern when the observer 
moves is due to the parallax 
present because the observer's 
eyes are not focused on the 
scattering surface. For example, if 
the scatterer is several meters 
away from the observer and if the 
observer is nearsighted, then the 
observer's eyes are focused in 
front of the scatterer. As the 
observer's head moves to the left, 
for example, parallax causes the 
speckle pattern to appear to move 
to the right 

5.1 16 In each of these two cases 
humming creates a stroboscopic 
image of the TV screen or rotating 
disc on the retina. Each source has 
periodic changes in appearance. 
The disc turns. The TV has a 

recurring image because of the 
line-by-line, horizontal sweep of 
the electron beam exciting the 
screen. A correct humming 
frequency oscillates the head, and 
thus the eye, appropriately to bring 
the recurring image back to the 
same place on the retina, The 
image then looks frozen. If the 
humming is not at such a 
frequency, then the head and eye 
oscillations are out of synch with 
the TV or disc, and the recurring 
image appears to migrate. For 
example, if the humming is at a 
frequency slightly too high for a 
frozen image, then the pattern on 
the disc will appear to move 
backwards against the sense of 
rotation of the disc. 

5.117 The elliptical motion of the 
pendulum is seen because the eye 

covered with the darkened filter 
experiences a delay by several 
milliseconds in its perception of the 
pendulum's position. In the brain's 
interpretation of the pendulum 
positions perceived by the two 
eyes, the pendulum is placed 
either doser or further away than 
its true position. Thus, the 
pendulum swing is interpreted as 
being two dimensional rather than 
one dimensional. For example, 
suppose the pendulum is swinging 
to the right while viewed with the 
left eye having the darkened filter. 
The right eye perceives the true 
position of the pendulum, whereas 
the left eye perceives it as where it 
was several milliseconds 
previously. You mentally 
extrapolate the light rays from 
these two positions backward until 
they converge so that they make 
sense as having come from a 
single object. This extrapolation 
means the pendulum will appear to 
be further away than it really is. 

Answers 281 

When the pendulum swings back 
to the left, a similar lag in 
perception occurs for the covered 
eye, and the brain interprets the 
pendulum as being doser than it 
really is. Overall, the pendulum 
appears to swing in an ellipse as in 
the right- mo st sketch of Figure 
5.117. The cause of the visual 
latency is not well understood. One 
analogue for the visual system is a 
series of delay line filters in which 
the time resolution of the system is 
improved by an increased 
feedback signal when the eye is 
subjected to greater illumination. A 
decrease in illumination reduces 
the feedback and thereby worsens 
the time resolution. 

5.118 The entire screen of the 

TV is not continuously lit, but is 
constantly swept horizontally line 
by line with the electron beam in 
the TV tube. The sweeping light 
can act as a stroboscope in lighting 
the top, causing you to see a 
frozen image of the top surface, or 
an image that turns one way or 
another, all depending on how the 
sweep frequency compares with 
the rotation rate of the top. 

5.119 Rods {which are primarily 
used in low levels of illumination) 
are packed the densest compared 
to the cones (which are for greater 
levels of illumination) toward the 
periphery of the retina. Staring 
directly at a star places its image 
on the fovea, in which there are no 
rods. Jumping your eyes away 
from the star sweeps the star's 
image across the greater packing 
of rods and enhances the 
perception of the star, 

5.120 Blue arcs are still under 
research. Although their cause is 
poorly understood, they appear to 
result from neurones excited by 

those axons directly stimulated. 
Suppose a stimulating light excites 
a particular set of photoreceptors 
that are linked to a particular set of 
ganglion axons. That set of axons 
can then excite other nearby 
neurones, which then stimulate the 
photoreceptors to which they are 
linked. The result is an apparent 
arc of stimulation stretching away 
from and around the fovea (the 
central pitlike region on the retina) 
with one end on the point under 
direct stimulation. The cause of the 
blueness has not been discovered. 

5.121 Apparently the production 
mechanism for phosphenes is not 
understood at all, because there 
has been almost no work 
published on modeling the 
phenomenon. The physical source 
has not even been identified 
conclusively, although some 
research has shown direct 
electrical stimulation of the 
occipital lobe at the rear of the 
brain can result in phosphene 

5.122 All the lamps should turn 
on at the same time because the 
lag of electricity is imperceptible. 
However, the street lamps at an 
intersection appear to turn on 
sooner because they collectively 
provide more light to the observer 
and therefore suffer less visual 
latency (FC 5.117) than the street 
lamps between the intersections. 

5.123 and 5.125 The elaborate 

network of blood vessels on the 
retina creates distinct shadows on 
the retina, but those shadows are 
rarely seen because the brain 
ignores any constant image from 
the eye. The vessels remain fixed 
with respect to the retina, their 
shadows remain constant, and 
thus you do not "see" the 

shadows. Exceptions occur in two 
cases. Upon first opening your 
eyes in the morning, the sudden 
casting of these shadows is a 
change and thus will be seen 
briefly until the brain fades out the 
information as being from a 
constant image. The other 
exception is that the blood cells 
carried by the retinal capillaries 
can cast shadows that are seen 
because the cells jerk their way 
through the capillaries. These cell 
shadows are the jerky specks in 
your field of view when you stare at 
a featureless illuminated area. 

5.124 The cause of these 
geometric designs is not well 
understood and is currently being 
researched. They could develop at 
the retina or in the neural 
pathways. They could also depend 
on the interaction of the 
information of one eye with that of 
the other eye. One type of pattern, 
roughly geometric but lacking 
precision and complexity, appears 
to be dependent on monocular 
vision. The more complex patterns, 
on the other hand, appear to result 
in part from binocular vision. 

5.125 See FC 5.124. 

5.126 Vision in bright light is by 
the cones on the retina, whereas in 
low illumination vision is by the 
rods. These do not have the same 
spectral response. The peak 
response of the cones is in the 
yellow (corresponding to a 
wavelength of light of about 0.56 
micron) with a much lower 
response in the blue. The rods 
respond best in the green 
(wavelength of about 0.50 micron 
for peak response) and have a 
much lower response in the red. If 
you observe red and blue while the 
room illumination dims from being 

282 Flying circus off physics with answers 

initially bright, your vision shifts 
from using the cones to the rods, 
and the relative response to the 
blues and reds changes 

5.1 27 The bright and dark bands, 
Mach bands, are illusionary. They 
can be photographed in the sense 
that an observer sees the illusion 
as readily in a photograph of a 
shadow edge as with a real 
shadow edge, The current theory 
for the band production involves an 
inhibitory effect in the neural 
network of photoreceptors being 
stimulated by the incident light 
near the shadow edge. In short, 
the signal of a firing photoreceptor 
inhibits the signal of a neighboring 
photoreceptor also being 
stimulated. Consider a shadow 
edge on the retina. On one side, 
say the left, the retina received a 
uniform bright illumination. On the 
other side, the right one, the 
illumination is uniformly dimmer, in 
a short intermediate region, the 
illumination drops from the bright 
level to the dim level . On the bright 
side of this intermediate, region a 
bright Mach band appears 
whereas a dark one appears on 
the dim side. In the uniformly lit 
region all of the photoreceptors are 
inhibited by their neighbors. So, 
the signal level from this area is 
less than would be expected if 
there were no inhibition. A 
photoreceptor on the edge of the 
intermediate region is less 
inhibited because on one side, in 
the intermediate region, there is 
less illumination. Hence a bright 
band is perceived there. A 
photoreceptor on the other edge of 
the intermediate region, that is, 
bordering the uniformly dim area, 
is more inhibited than the receptors 
in the dim area because of the 

illumination in the intermediate 
region. Hence, a dark band is 
perceived there. 

5.128 The Land effect is not well 
understood in its complete process 
but is currently modeled by 
supposing that there are three 
types of cones on the retina that 
are distinguished by where in the 
visible range their peak response 
lies: one type each for the 
middle-wavelength, and 
long-wavelength ranges. When 
you observe a color scene, each 
set of cones somehow measures 
the reflectance of light from the 
scene in those three wavelength 
ranges, compares those 
reflectances, and then creates 
your color sensations. Color 
results from the black-and-white 
slides described in FC 5.128 
because the reflectance 
information at two different 
wavelengths is apparently 
sufficient to trigger color 
responses. Hence, the colors you 
perceive may be almost 
independent of the wavelength of 
the light you receive. 

5.129 The colored edges of the 
light source are due to the 
chromatic abberation of the eye. In 
the arrangement of Figure 5.129, 
the finger blocks the right side of 
the viewing eye such that the 
observed light rays from the 
window enter the eye only on the 
left side of the eye. Upon entering 
the eye, the red rays are refracted 
slightly less than the blue rays. 
Although the aberration is normally 
not noticeable, the partial blocking 
of the eye with the finger allows the 
viewer to distinguish the different 
images of the window edge for 
different colors. Consider light 

radiated from the right side of the 
window and entering the left side of 
the eye. The small difference in 
refraction for red and blue light 
results in the red image of the 
window edge being slightly to the 
left of the blue image on the retina. 
The blue image is lost in the white 
light coming from the window 
somewhat away from the edge. 
Thus, the observer sees a reddish 
window edge. A similar separation 
of colors occurs for the left side of 
the window, but this time the red 
image happens to be lost in the 
white light from the rest of the 
window, and the viewer is left with 
a bluish edge, 

5.130 Previous to current 
research, the colors were thought 
to result from the difference in 
times needed to turn on the color 
responses in the visual pathway 
after the observer viewed 
daftness. In particular, the 
theories concluded that red turned 
on slightly sooner than blue, and 
thus the leading edge of the white 
area was red. However, recent 
research indicates no such 
difference in turn-on times for the 
different colors. One of the current 
theories about the color response 
to the disc is that the pattern of its 
intensity variations either mimics or 
creates a photoreceptor firing 
pattern that mimics the brain's 
color coding. In other words, the 
proper pattern of intensity changes 
sends a Morse-code-like signal to 
the brain telling the brain it sees a 
particular color for that particular 
code. As in FC 5.128, seeing red 
does not necessarily mean that 
you are viewing light with a 
wavelength of about 0.6 microns. 
Color perception appears to be far 
more intricate. 

Answers 203 

5.131 Whereas the blues and 
greens from the fluorescent lamps 
turn off during part of the cycle in 
the 120 cycle-per- second 
stimulation of the lamp, the yellows 
and reds (if the lamp has much 
red) do not. As a result, a spinning 
black-and-white disc or a spinning 
coin will reflect colors to the 
observer that change with time. 
The difference in the color duration 
comes from the three types of 
emissions present in the lamp's 
output. The short-lived blues and 
greens come primarily from the 
mercury emission lines (which 
have very short lifetimes) and a 
phosphorescence also with a short 
lifetime. The yellows come mostly 
from a long-lived fluorescence 
from the same phosphor. 

5.132 The picture on a TV 
screen is not created whole but is 
quickly produced by the electron 
beam in the TV tube moving 
horizontally line by line downward 
until the bottom of the screen is 
reached. The sweep is so fast that 
you don't perceive it. If you swing 
your eyes to the right, each 
horizontal sweep leaves an image 
on the retina for about 75 msec or 
so. Because your eyes move 
during the beam's line sweep, the 
lasting image of a particular line is 
slightly to the right of the line just 
below it because the top one was 
made slightly sooner. The overall 
lasting image of the screen is 
therefore tilted as shown in Figure 
5.132. Multiple images are 
observed because during the full 
swing of your head the electron 
gun has filled the screen several 
times, each full image giving you 
an image to carry briefly off to the 

5.133 Most of the stereoscopic 

illusions depend on imitating 
normal binocular vision that gives 
depth in our normal viewing. In the 
stereoscope (the device now 
bought only for children but that 
once provided much evening 
entertainment for all) contains two 
photographs shot with camera 
positions separated by a few 
centimeters and with an 
appropriate angle adjustment to 
mimic our normal viewing. When 
you examine the photographs with 
the stereoscope, the different 
images are fused to make a single 
image with apparent depth. 
Three-dimensional movies 
depended on providing a similar 
shift in perspective for each eye. 
For example, the two images might 
be projected, one in blue and the 
other in red. The audience would 
then wear glasses with blue 
cellophane over one eye and red 
cellophane over the other. Again 
the two images are fused to 
provide a single one with depth. 
Different polarizations of the 
projected light could be used 
instead of the different colors. The 
glasses would then have the left 
side passing a different 
polarization than the right side. 
Three-dimensional postcards 
employ a single picture but provide 
different images for the left and 
right eye by a grid of prisms or 
furrows in a plastic sheet 
overlaying the photograph. 
Because of the tilted surfaces of 
the plastic overlay, the left eye 
receives a different perspective of 
the photograph than does the right 
eye, resulting in depth when the 
two are fused. 

The illusion that the red letters 
on a blue background are in front 
of the background appears to be 
due to chromatic aberration of the 

eye. With the object viewed so that 
its light rays enter at some angle to 
the central axis of the eye, the blue 
rays are refracted more than the 
red rays. This difference means 
that only one of the colors can be 
brought to focus on the retina. The 
image in the other color will be a 
blur to one side of the sharp image. 
For example, consider viewing 
equidistant red and blue points on 
a card somewhere in front of your 
eyes. Suppose the red point is in 
focus. Its image lies further from 
the center of the head than does 
the blue blur from the blue point. 
Such a displacement in normal 
binocular viewing is interpreted as 
indicating the red point is closer 
than the blue point. 

5.134 Exactly why the illusion is 
seen is not clear, even after much 
debate in the literature on the 
subject. The enlargement has 
nothing to do with atmospheric 
conditions (indeed, refraction 
decreases the size of the moon, as 
discussed in PC 5.18). Instead, the 
illusion appears to depend on the 
space between the moon and the 
horizon. For a very large space, 
corresponding to a large angular 
elevation of the moon, the moon 
appears to be its proper angular 
size of 0.5 arc degree. As the 
moon descends and the space 
between it and the horizon (or the 
objects on the horizon) decreases, 
the moon appears to grow. 

5.135 The rays are actually 

parallel. Their apparent meeting at 
some point in the distance is an 
illusion. A similar illusion can be 
seen by standing in the middle of a 
very long, straight train track. If you 
pretend not to know about the 
distant track, it will appear to 
converge at some point on the 

284 Flying circus off physics with answers 


5.136 If you bisect the moon with 
a long stick, it will cut through the 
sun just as it should. But without 
such a reference, the mentally 
extrapolated line bisecting the 
moon will miss the sun. The illusion 
results from your perception of the 
sky as an overhead spherical 

5.137 The apparent bending of 
the searchlight beam is an illusion 
that depends on the illusion of the 
sky being an overhead dome just 
as in the previous problem. 
Holding a straight edge along your 
view of the beam will convince you 
the beam is really straight. 

5.138 Apparently an explanation 

of why the illusion occurs is not 
available. It is a surprising illusion 
in that previous to its published 
description, an elevated object 
equidistant with a similar level 
object was thought to always 
appear to be more distant. 

5.139 Whiteout can come in two 
different cases. A ground blizzard 
may whip up all the loose snow to 
limit visibility to just a few feet With 
such restricted visibility, a person 
can become lost in the swirling 
snow after walking just a few feet. 
Another type of whiteout is the 
elimination of visual clues when 
the ground is covered with snow 
and the sky is filled with white 
clouds The lighting becomes so 
diffused that no shadows are cast, 
and bcth the snow and the clouds 
appear to vanish. One might then 
have the impression of walking or 
skiing over a vast white emptiness. 
Permanent blindness might also 
result from constant viewing of 
snowfieids under intense light 
because the visible and ultraviolet 

light can destroy part of the visual 
process. (W. C. Burkitt, personal 

5.140 For an example, consider 
an astronaut viewing the earth 
from an orbit about 800 km (500 
mi) above the surface. If he uses 
only his eyes rather than a 
telescope, signs of intelligent life 
are very difficult to detect. His eyes 
are diffraction-limited in their 
resolution, that is, the limit on how 
small an object he can resolve is 
imposed by the diffraction of light 
through the circular opening to the 
eye. (Some animals are limited in 
their resolution because of the 
photoreceptor spacing on their 
retinas. An image smaller than that 
spacing cannot be resolved.) For a 
typical human eye the smallest 
object that can be resolved 
occupies about 0.0005 radian in 
the field of view. This limit means 
that the astronaut can just barely 
resolve objects of about one 
kilometer on the earth's surface. 
Very few man-made features can 
be recognized with such 
resolution. Primarily the telltale 
signs of intelligent life are 
geometric structures, such as long 
straight superhighways. In an 
examination of thousands of 
photos from the Tiros and Nimbus 
meteorological satellites having 
resolution limits of about 0.2 to 2.0 
km, only a highway and an 
orthogonal grid of some Canadian 
loggers were recognized. 

5.141 A point source of light in a 
dark room appears as a light streak 

in the Christmas tree ball because 
the eye can accept reflected light 
rays in a significant range of 
angles. Mentally extrapolating 
those rays back into the ball gives 
the impression that the light 

originates from a line source. 
When the room lights are turned 
on, the pupil size gets cut in half 
and that acceptance range is 
decreased enough that the 
apparent line source is shrunk to a 

5.142 The Moire patterns appear 
according to how elements in the 
two overlaying grids, cloth, and so 
on, fall in step. For example, the 
comb and its reflection will 
periodically have teeth exactly 
overlapping, partially overlapping, 
and then not overlappi ng at all . The 
resulting Moire pattern appears to 
be an enlargement of the teeth in 
the comb, or at least an 
enlargement of the same type of 
periodic structure. 

6.1 Roughly speaking, the 

effects of current through the 
human body are the following: 

less than 0.01 amp— tingling or 


0.02amp— painful and cannot let 

go (see FC 6.3) 

0.03 amp— breathing disturbed 

0.07 amp— breathing very 


0.1 amp— death due to 


more than 0.2 amp— no 

fibrillation, but severe burning 

and no breathing 

The intermediate range of 0.1 to 
0.2 amp is strangely enough the 
most lethal range for common 
situations, because this level of 
current initiates fibrillation of the 
heart which is an uncontrolled, 
spastic twitching of the heart. The 
resulting disruption of blood flow 
quickly results in death. Above 0.2 
amp the heart is merely stopped, 
and normal first aid procedure can 
restart if. But another, controlled 

Answers 285 

electrical shock is the only way to 
stop fibrillation. Hence, the 0.1 to 
0.2 amp range is more deadly than 
larger currents. 

The current passing through a 
victim is usually determined by the 
skin resistance, which ranges from 
about 1000 ohms for wet skin to 
about 500,000 ohms for dry skin. 
The internal resistance is smaller, 
being between 100 and 500 ohms. 
Touching voltages higher than 
about 240 V usually results in 
current puncturing the skin. Often a 
person grabs a wire that has 
sufficient current to contract his 
hand muscles onto the wire. That 
level is initially not lethal, but the 
skin resistance drops with time 
until the lethal level of 0.1 amp is 
finally achieved. If you find 
someone "frozen" to a live wire but 
still alive, you should remove that 
person as quickly as possible 
without endangering yourself, or 
eventually the person will die. 

6.2 An electric potential lies 
between the two metals where 
they contact, owing to the 
difference in the energy levels of 
the conduction electrons on the 
metals. When the frog leg touched 
the railing, a complete circuit 
through the railing, support, and 
leg was made, and electricity 
(those conduction electrons) 
flowed through the circuit. The 
current excited the muscles in the 
leg, forcing the leg to contract. 

6.3 The wire does not capture 
your hand with an electrical force. 
Instead, the current through the 
hand muscles causes the hand 
muscles to contract, clamping your 
hand around the wire. Electricians 
working with live or potentially live 
wires often use the back of their 
hands or fingers to move the wires. 

If the touch does draw current, the 
muscle contraction then throws the 
hand away from the wire. 

6.4 When activated by a nerve 
signal, the biological cells called 
electroplaques suddenly allow an 
ion flow — a current— across their 
membranes. The electric fish have 
a series of the cells from head to 
tail, and the combined electric 
potential from each during the ion 
flow (about 0.15 V between the 
interior and exterior of the cells) 
creates a voltage difference 
between head and tail. Many such 
series of cells are "wired" in 
parallel in the fish to provide 
sufficient amperage to flow 
externally from its head to tail to 
stun or kill its food or enemy. For 
example, the Torpedo nobiliana 
(a saltwater giant ray) has about 
1000 electroplaques in series and 
about 2000 series in parallel. Were 
all the electroplaques placed in 
series, not only would the fish be 
rather long, but also the current 
through the series would be large 
enough to destroy the cells. By 
using a parallel wiring of the series, 
the current through each cell is 
kept low without sacrificing the 
external current. Fresh- water 
electric fish have greater numbers 
of electroplaques in series 
because they need more 
head-to- tail voltage to force the 
same current through the higher 
resistance of fresh water. 

6.5 The microwaves are 
absorbed by the meat, mostly by 
the water in the meat, within a 
depth of one to several centimeters 
from the surface. The rate of 
absorption with depth depends on 
the frequency of the microwaves: 
the lower the frequency, the 
greater the depth. Most microwave 

ovens operate at a frequency of 
2450 MHz, which penetrates and 
heats primarily the first two 
centimeters of meat. A microwave 
oven is designed to bathe the meat 
with microwaves from essentially 
all directions. Provided the meat is 
not too large, the amount of 
radiation reaching the center of the 
meat from all directions could be 
greater than the amount absorbed 
in the first centimeter on any one 
side. As a result, the center would 
absorb more than the outside layer 
of meat and would cook sooner. 
However, the result could be just 
the opposite if the piece of meat is 
large, or if the oven does not bathe 
the meat, or if the operating 
frequency is high and thus the 
penetration depth is small 
compared to the size of the meat. 

6.6 The electrons move through 
the circuit at a relatively slow 
speed of 10- 4 m/s, but the 
signal — the change in the electric 
field along the wire— moves at 
nearly the speed of light. It is the 
signal rather than the actual 
electrons from the wire in the 
switch that must reach the light. 
The signal may reach the filament 
in the bulb in as little as a 
nanosecond (10- 9 s), hardly 
enough time to bother with. 
However, the filament must first be 
heated by the current through it 
before it can emit light. To emit 
visible light, the filament should be 
several thousand degrees Kelvin, 
and that temperature is typically 
reached 0.01 to 0.1 s after the 
switch is thrown. 

6.7 When the two materials (e.g., 
shoes and rug or cat's fur and 
glass) touch, electrons from one of 
the materials tunnel through the 
electrical potential barriers on the 

286 Flying circus of physics with answers 

surface to the other material. For 
example, when glass touches cat's 
fur, electrons tunnel from the glass 
surface to the furs surface. Since 
neither are good conductors, this 
tunneling occurs only where the 
materials actually touch. To obtain 
more transferred electrons, more 
parts of the materials should be put 
in contact Rubbing the surfaces 
together is the most convenient 
way of putting more parts of the 
materials in contact to obtain a 
greater transfer of electrons. The 
material losing the electrons is left 
positively charged; the other 
material becomes negatively 
charged. Jf the air is damp, the 
excess charge drains quickly to the 
airborne water drops. Smoke 
particles could also remove the 
charge. Without such discharge, 
normal contact of materials can 
produce fairly high potentials. For 
example, sliding across a car seat 
and stepping outside can leave 
you 15 kV higher than ground 

6.8 The apparatus must be 
arranged such that the water 
streams falling from the nozzles 
break into drops at about the level 
of the top cans. Initially, when the 
water first begins to fall, one can is 
charged negatively slightly more 
than the other can. Which can is 
more negative is sheer chance, 
because the initial charge 
difference is due to the charging by 
either cosmic rays or the earth's 
natural radioactivity. Suppose, for 
illustration, that the bottom-left can 
in Figure 6.8 is more negative. 
Then the top-right can will also be 
more negative than the top- left can 
because of the wiring. The 
right-hand stream is polarized as it 
falls through the top can. If the 
drops develop just then, the drops 

will be positive, the negative 
charge in the stream being 
repelled by the can around the 
stream. Since those drops fall into 
the bottom- right can, that can 
becomes more positive than 
before. Although the initial voltage 
difference between the bottom 
cans is trivial, some homemade 
Kelvin droppers develop a 
potential difference of as much as 
15 kV. 

6.9 The liquid stream breakup 
was first explained by Rayleigh, 
who showed that disturbances to 
the emerging stream would result 
in waves around the stream axis, 
these waves growing exponentially 
in amplitude until the stream 
disintegrated. Once broken up, the 
water pulls together by surface 
tension to form drops. The breakup 
can be avoided or delayed by the 
presence of a charged rod 
because of the resulting induced 
charge separation in the stream. 
For example, if the rod is positive, 
then the stream side nearest the 
rod is negative and that side 
furtherest from the rod is positive 
because the rod's electric field has 
forced electrons to flow across the 
stream to be nearer the rod. With 
such a charge separation, the 
stream is less likely to break into 
drops. Suppose there is a 
separation into drops. Consider 
two freshly produced drops lying 
along a line radially extended from 
the rod. Because of the induced 
separation of charge in the drops, 
their adjacent side would be 
oppositely charged, and the two 
drops would attract each other, 
Thus, the drops do not form in the 
first place. If the rod is highly 
charged, then the stream's near 
side is so attracted to the rod that 
the stream is bent from its normal 


6.10 The charging of wire 
fences, airplanes, and similar 
metallic objects by blowing snow is 
the result of the same type of 
electron transfer as in FC 6.7. The 
metallic objects receive electrons 
from the snow particles and 
become negatively charged. 

6.11 The tape separation 
appears to cause a separation of 
charge, the adhesive layer carrying 
away a different charge than the 
top surface of the tape to which it 
had just been attached. The glow 
is an electrical discharge between 
the two surfaces of tape that have 
just been separated. 

6.12 The sugar is charged as in 

FC 6,10 and 6.7 when it is sifted. 
Since the falling sugar grains then 
have like charge, they repel each 
other, and some of the sugar is 
pushed to the side. 

6.13 Contact between the tires 
and the road leaves the tires 
negatively charged. As the tires 
rotate and become uniformly 
charged, the negative electrons in 
the metal body and frame are 
repelled by the tires, leaving the 
body area near the tires positively 
charged. Sparking between a 
particular part of the car and some 
nearby grounded or oppositely 
charged body is then possible. The 
sparking would be merely a 
nuisance except in the case of 
gasoline trucks where gasoline 
fumes may be ignited. Years ago 
chains were dragged from the 
truck's body and on the ground in 
the belief that the chains would 
continuously discharge the truck. 
The chain would drain some of the 
electrons from the truck's body, but 
that would not leave the truck 

Answers 287 

neutral and thus safe because it 
would then be positively changed 
and hence still susceptible to 

6.14 Details of the charge 
separation in the splashing of 
water are not presently well 
understood. In the nineteenth 
century, however, Lenard showed 
that the larger drops floating in the 
air near the splashing were 
positively charged, whereas the 
smaller drops were negatively 
charged. Since the larger drops 
settle more quickly than the 
smaller ones, the air is left with 
negatively charged drops and a 
rather large electric field. 

6.15 Apparently the effect of 
charge on a human being is not 
fully verified, much less explained. 

6.16 The basic force preventing 
you from falling through your 

shoes t the floor, and the ground is 
the electrical repulsion between 
the atoms in each set of adjacent 
surfaces. (Also see FC 7.24.) 

6.17 Four types of forces may 
hold a powder together. If the 
particles are less than about 50 
microns, van der Waal's force (an 
attractive force between atoms) 
may be important. Electrostatic 
attraction of unlike charges on the 
powder grains can also hold the 
grains together. If the powder is 
damp, then the water can bond the 
grains by essentially a surface 
tension type of force. (But if there is 
too much water, the powder 
becomes just a slush,) And finally, 
if the particles are irregular in 
shape, their interlocking holds 
them together. Current research 
on powders and crumb formation 
attempts to explain the bulk 
cohesion of certain powders in 
terms of these forces on the 

microscopic scale. 

6.18 Static electricity on the 
plastic wrap causes the wrap to 
cling to itself and to most food 
containers. For example, if the 
layer of plastic next to a metal wall 
has an excess of electrons, then it 
repels the electrons in the metal. 
The area next to the wrap is thus 
left positive and attracts the wrap. 
Since the wrap is not a good 
conductor of electricity, its static 
charge does not readily drain to the 
metal. As a result, the plastic 
clings. Some of the static charge 
originates when the plastic roll is 
being manufactured. Indeed, 
avoiding static charge during the 
production would be difficult. More 
charge separation can occur when 
you pull the plastic off the roll: a 
faster pull produces more charge. 
Humid air or a wet container drains 
the static charge and thus reduces 
the cling. 

6.19 The ink in the dollar bill 

contains magnetic salts, probably 
iron salts, that are attracted to one 
of the magnet's poles. 

6.20 The fluid in the leveler is 
diamagnetic, that is, when it is 
placed in a magnetic field, it 
produces a magnetic field in the 
opposite sense. The fluid is 
repulsed from the magnet, thereby 
forcing the bubble toward the 

6.21 A changing current in the 
coil creates an accompanying 
changing magnetic field in which 
the ring lies. That field in turn 
creates a current in the ring such 
that the magnetic field of the 
induced current is opposed to the 
magnetic field of the coil. The 
second magnetic field supports the 
ring in the first magnetic field. If 
current is switched on, the sudden 

change of current in the coil 

induces a larger current in the ring 
and thus a larger magnetic field 
that may be sufficient to send the 
ring upward. 

6.22 The alternating magnetic 
field induces currents in both the 
fixed sheet and the disc. Without 
the fixed sheet, the part of the disc 
over the magnet would fully have 
such induced currents, whose flow 
would be in such a direction that 
the magnetic field created by the 
flow would cause repulsion of the 
disc by the magnetic field from 
the magnet. Without the fixed 
sheet, the disc would therefore be 
repulsed by the magnet. With the 
sheet in place, however, the 
induced currents in it and in the 
unshaded portion of the disc attract 
each other (the magnetic field of 
one of the currents forces the other 
current closer), and the disc is 
continuously rotated. 

6.23 The changing magnetic 
field from the rotating magnet 
induces currents in the aluminum 
disc. These currents in turn set up 
their own magnetic field. The 
interaction of the two fields creates 
a torque on the disc, causing it to 
turn in the same sense as the 
rotating magnet. 

6.24 Why not build this simple 
device to see if it is truly workable? 
If the magnetic field is strong 
enough to start the ball up the 
inclined plane, won't if be strong 
enough to prevent the ball from 
sliding down the ramp underneath 
the plane? 

6.25 The penetration depth of 
radio waves through the 
ionosphere depends on the 
frequency of the waves. The 
ionosphere is transparent to the 

288 Flying circus off physics with answers 

relatively high frequency waves 
used h TV and FM radio 
transmissions. However, the lower 
frequency waves used in AM radio 
transmissions are reflected from 
the ionosphere. Thus, to receive a 
particular TV or FM program, the 
receiver must be near the 
transmitter to receive either a 
direct signal or at least a signal 
reflected from the environment 
(buildings, etc). In the AM case, 
the receiver can be distant since it 
can use the signal reflected from 
the ionosphere. Occasionally the 
higher frequency signals are 
reflected from the ionosphere and 
can be received at surprising 
distances. Such reflections are 
likely due to the increased 
ionization in the ionosphere during 
meteor showers or during what is 
called sporadic-E conditions. The 
latter increase in ionization is not 
currently understood very well, but 
may be linked to increased 
radiation from the sun. The 
reflecting level of AM signals rises 
at night because the lack of 
sunlight decreases the ionization 
of the molecules on the lower side 
of the ionosphere. With a higher 
reflecting level, the AM signals 
travel further around the curve of 
the earth. To avoid an 
unmanageable mess of signals, 
the FCC requires most stations to 
cut their power or to leave the air 
during the night. 

6.26 The receiving circuit 
resonates at a particular frequency 
that depends on the magnitudes of 
the capacitance (of the capacitor) 
and the inductance (of the coil) . By 
varying the contact on the coil, the 
inductance can be altered, thus 
changing the frequency at which 
the circuit responds. The incoming 
signal is sinusoidal. Since the 

average power absorbed from a 
sinusoidal signal is zero, the 
listener would hear nothing were 
the signal not changed. The 
contact between the metal 
"whisker" and the crystal allows 
the current to flow in one direction 
only. Thus, the signal is rectified, 
because half the sinusoidal (say 
the negative part) is removed. With 
only half the sinusoidal wave in the 
circuit, the average power 
absorbed is no longer zero, and 
the listener can hear the signal. 

6.27 The airplane reflects the TV 
signal to your antenna slightly later 
than the direct signal is received. 
The direct signal places an image 
on the screen; the later reflected 
signal places another, fainter 
image to the right on the screen —a 
ghost image— that changes as the 
airplane continues to move. The 
ghost is to the right because the 
electron gun producing the screen 
image scans from your left to your 

6.28 The AM transmitters have 
vertical antennas. If the radio wave 
is directly received by the car's 
antenna, the electric field in that 
wave is polarized along the sense 
of the transmitting antenna, in 
other words, vertically. To gain the 
maximum signal strength, the 
receiving antenna should also be 

6.29 In the FM region the 
appearance of the same signal at 
multiple places across the dial is 
due to the nonlinear response of 
the receiver in the presence of a 
very strong signal; the effect is 
called cross modulation. In the AM 
region, a signal can be 
overwhelmed by a stronger one 
normally at a different frequency if 
the receiver is near the transmitter 

of the second signal. Both the 
transmitter and the receiver work in 
a rather narrow frequency range. 
However, neither is exactly at a 
single frequency. For example, a 
transmitter may be primarily at 
1 1 ,000 kHz, but it may also be 
transmitting a fraction of its power 
at 1 1,500 kHz. A distant receiver 
would not sufficiently amplify this 
very weak signal at 1 1 ,500 kHz for it 
to be heard. If a nearby receiver is 
tuned to another station whose 
primary frequency is at 11,500, it 
may also receive and sufficiently 
amplify the undesirable signal from 
the first station. 

6.30 Low-energy solar electrons 
(with energies in the hundreds of 
electron volts) are swept into the 
plasma tail on the antisolar side of 
the earth, are somehow increased 
in energy (to several thousand 
electron volts), and then are 
directed into the atmosphere near 
the poles by the earth's 
field lines. Those lines enter and 
leave the earth at the magnetic 
poles, which are offset somewhat 
from the geophysical poles about 
which the earth spins. The 
energized solar electrons enter the 
atmosphere in an oval around the 
magnetic poles and excite nitrogen 
molecules and oxygen atoms by 
collision. Green light is emitted by 
deexciting atomic oxygen at 
altitudes from 100 to 150 km. 
Higher atomic oxygen produces a 
strong red light. Red light also 
comes from deexciting molecular 
nitrogen. These colors are 
observed in the ovals around the 
magnetic poles along the 
geomagnetic latitudes around 70°. 
With the north geomagnetic pole in 
Canada, this arrangement places 
auroras over southern Canada and 
northern United States. The same 

Answers 289 

geophysical latitude over Siberia is 
at a lower geomagnetic latitude 
and has fewer auroras. 

6.31 Lightning sends out 

electromagnetic pulses that are 
first heard directly as clicks on the 
detectors. Part of the pulse waves 
travel upward. Those waves 
traveling upward are concentrated 
into a beam in the ionosphere and 
are then bent over such that the 
beam travels along one of the 
magnetic field lines of the earth. 
When the beam reaches the 
opposite pole region, it is reflected 
by the stronger magnetic fields and 
returns along a field line to near the 
point of origin. But not all of the 
beam travels at the same speed: 
the higher frequency components 
travel faster. When the returning 
beam is detected, the higher 
frequencies are heard first, and 
then progressively lower 
frequencies arrive. Instead of the 
original click being repeated, this 
electromagnetic echo lasts longer 
and descends in pitch. 

6.32 In a normal lightning stroke 
the charge distribution in the cloud 
is the following: small amount of 
positive charge at the base, large 
amount of negative charge in the 
lower middle, and large amount of 
positive charge in the top. The 
stroke begins with a discharge 
between the base and the lower 
middle, bringing electrons down to 
the base. This discharge proceeds 
from the base downward by a 
"stepped leader," which jumps in 
lengths of 50 m, pauses about 50 
pd, and then jumps again. Each 
time, negative charge drains from 
the cloud to the bottom of the 
channel. Only the lower tip of the 
leader is visible, but the motion is 
so rapid at this stage and the 

following stages of the stroke, that 
the whole process appears to be 
luminous. The leader is crooked 
because the path of the 
descending channel is deviated by 
pockets of positive charge in the 
air. If a pocket is sufficiently strong, 
the leader may even be turned 

When the leader is near the 
ground, the electric field near 
sharp points is sufficiently high that 
electrical breakdown occurs and a 
positive return stroke starts upward 
to meet the leader. The point of 
meeting is highly luminous as the 
negative leader is neutralized and 
its electrons are brought to ground. 
This region of high luminosity and 
current propagates up the leader 
channel until it reaches the cloud, 
but the observer cannot resolve 
the rapid motion and sees a 
continuously luminous channel. 
The leader's trip down takes about 
20 ms, whereas the return stroke 
takes only 100 ps. The light comes 
from the center of the leader 
channel, probably from a core no 
wider than a few centimeters. 

6.33 The earth's electric field, 
which lies between the negatively 
charged surface and the positively 
charged upper atmosphere, should 
be discharged in 5 min or less 
because of the constant ionization 
of air molecules by cosmic rays 
and the earth's natural 
radioactivity. Some of the electrons 
from the ionization move to the 
upper atmosphere where at an 
altitude of about 50 km the 
conductivity is so good that the 
atmosphere is essentially a 
spherical conductor. The rising 
electrons will neutralize this 
positive conductor. Similarly, some 
of the positive ions from the 
ionization descend to the negative 

ground to neutralize it. Because 
the worldwide current resulting 
from the ionization is about 1800 
amps, both the ground and the 
upper atmosphere should be 
discharged in a few minutes. They 
are not, because the worldwide 
lightning activity is constantly 
recharging the earth with 

There may be a 200- V 
difference between the heights of 
your feet and nose, but your body 
is such a relatively good conductor 
that all of it is at essentially the 
same potential. Hence, no 
significant voltage difference exists 
across your body. 

6.34 The cloud-to-air stroke 
terminates in a pocket of positive 
charge in the air. The ribbon 
lightning occurs when the wind is 
strong enough to move the ionized 
channel noticeably between 
strokes when more than just the 
leader and return strokes run 
between the cloud and ground. 
Bead lightning is not well 
understood. It may sometimes 
occur when the stroke is partially 
obscured by rain so that the 
observer is not blinded by the flash, 
Then, as the luminosity dies away, 
those portions of the stroke running 
along the observer's line of sight will 
last slightly longer because of the 
greater amount of light when such a 
portion is viewed on end. However, 
the bright beads may also occur for 
different, and as yet unknown, 

6.35 The nature of ball lightning 
is still current research, and any 
explanation given here may be 
soon proven wrong. Probably the 
best explanation to date is that the 
ball is a plasma ball that is fed 
energy from external 
electromagnetic waves. Some 

290 Flying circus of physics with answers 

electrical activity of a 
thunderstorm, lightning, or point 
discharge initiates ionization of the 
air or of a vapor gas (if something 
such as a metal conductor has 
been struck). The ionized gas 
remains integral because of its 
overall electrical neutrality, but 
grows to some equilibrium size 
because it absorbs energy from 
natural radio waves. Such waves 
are known to be generated either 
at the clouds or at the ground 
during intense electrical storms. 
The environment of the ball 
imposes constraints on the radio 
waves, creating standing waves, 
and the ball absorbs energy from 
an antinode in such a standing 
wave. An external source of 
energy like this is appealing, 
because the relatively long-living 
luminosity of the balls is otherwise 
very difficult to explain. If the light is 
only from an internal source of 
energy, and if a nuclear fireball is 
scaled down to the size of ball 
lightning in order to put an upper 
limit on such Internal energy, the 
ball would glow for no more than 
about 0.01 s instead of the 
reported several seconds, 

6.36 The H-bomb lightning 
strokes may have resulted from the 
charge produced when gamma 
rays from the burst scattered 
electrons from the air molecules. 
The leaders for the strokes 
apparently propagated upward 
from the instrumentation structures 
near the surface. Similar upward 
propagating leaders, which 
contest with the downward 
leaders of normal lightning (FC 
6.32), have been seen starting 
from tall structures such as the 
Empire State Building. Since the 
leaders run upward, so does the 

6.37 The hot lava hitting the 
seawater sends positively charged 
steam upward. After sufficient 
charge separation has occurred, 
the clouds of steam discharge 
back to the ocean, allowing 
electrons to flow upward through 
the ionization column. The upward 
flow of electrons is opposite the 
situation with normal lightning (FC 

6.38 Earthquake lightning is not 
well understood. Recently it has 
been attributed to piezoelectric 
fields created when seismic waves 
propagate through either the 
surface or low-lying rocks, (In the 
piezoelectric effect, electric fields 
are created in a material when the 
material is placed under stress. 
The diamond used in modern 
record players is an example of a 
piezoelectric crystal whose electric 
fields are created by the stress 
from the bumps in the record 
grooves.) Supposedly such electric 
fields would be large enough to 
cause atmospheric discharges on 
the surfaces. However, details and 
proof of this model are currently 

6.39 The pointed wire was to 
provide a sufficiently high electric 
field that enough current would be 
attracted to allow Franklin to do his 
experiments. (The sharper the 
object, the greater the electric field 
is around it.) The silk ribbon was 
insulation between himself and the 
wet conducting twine. The key 
provided several sharp points for 
visible discharge of the electron 
current descending the twine. 
Often Franklin is pictured doing 
this experiment during a lightning 
storm. He was never that stupid. A 
lightning strike to the kite would 
have destroyed the kite, the twine, 

and possibly Franklin, regardless 
of a trivial piece of silk. In actuality, 
Franklin flew his kite before the full 
storm arrived. 

6.40 The purpose of the lightning 
rod is to provide a safe route to 
ground for the descending current. 
The sharp point has a high electric 
field around it and can initiate the 
upward traveling channel that 
meets the downward traveling 
leader stroke (FC 6.32). Once 
contact is made, the electron 
current flows from the ionization 
channel and through the rod to the 
ground in which the rod is buried. 
The possibility of the stroke hitting 
the structure to which the rod is 
attached is thereby reduced. The 
lightning rod cannot appreciably 
discharge a passing cloud to avoid 
lightning because such discharge 
is too slow. The radioactive source 
proposed for the rods would have 
no effect and probably would prove 
to be dangerous if a lightning strike 
ruptured the source. 

6.41 If the tree is thoroughly wet, 
the current descends through the 
water sheath and leaves the tree 
unharmed. If not, the current may 
enter the tree to descend through 
the sap. The rapid heating and 
expansion of the sap then blows 
the tree apart. Oak is more 
susceptible to explosions than 
many other trees because it has 
rough bark. If the lightning strike 
occurs early in the rainstorm, it 
may find only the top part of an oak 
wet, whereas a smooth bark tree 
would be wet to the ground. The 
oak would be blown apart, and the 
smooth bark tree left untouched. 
Forest fires are initiated by 
lightning strokes in which there is a 
continuous current running through 
the lightning channel between the 

Answers 291 

main strokes, that is, between the 
first return stroke and the following 
ones. Since the continuous current 
is not always present, not a!! 
lightning strokes to trees would set 
the trees on fire. 

6.42 The high frequency current 

of a lightning strike does not 
penetrate the metal walls of a car, 
airplane, and the like, but stays on 
an outside layer of the metal. 
Barring a puncture to the fuel and 
the consequent explosion, the 
occupants in such a metal 
enclosure will probably not even 
know that they have been hit. 

6.43 At times the water droplets 
in the clouds are partially 
suspended by the local electric 
fields. A lightning stroke occurring 
then may decrease those fields, 
causing an enhanced fall of the 
droplets — a rain gush. As the 
electric fields regain their strength, 
the precipitation decreases. 

6.44 The rapid evaporation and 
expansion of the moisture on your 
skin blows your clothes and shoes 
off. You may be otherwise 
unharmed if little of the current 
entered your body. 

6.45 After reaching the ground, 

the lightning current spreads out 
and runs partially horizontal. If a 
cow stands as in Figure 6.45, an 
appreciable amount of the ground 
current enters the front legs and 
exits from the rear legs, 
electrocuting the cow. If you are 
caught outside during a 
thunderstorm, you should not lie 
down. If a strike hits nearby, the 
resulting electrical potential 
between your head and your feet 
may draw enough of the ground 
currents tc kill you. Since you also 
should not stand up, the best 


position is to squat. That way you 
keep your head low while 
minimizing the contact area with 
the ground. With minimal contact 
area, the possible electrical 
potential from one side of the 
contact area to the other is least, 
and you will draw the least ground 

6.46 and 6.48 Ground-level St. 
Elmo's fire and the Andes glow are 
both examples of corona discharge 

in which the electric field 
surrounding objects, usually 
pointed objects, is sufficiently high 
that electrical discharge can occur. 
The Andes glow is an especially 
strong type of corona, not fully 
understood yet. St. Elmo's fire can 
also occur on aircraft flying through 
rain or snow because of the 
charging discussed in FC 6.7, 
6.10? and 6.14. 

6.47 If a massive current enters 
a victim 1 s body, the person will 
likely die because of internal burns. 
But the lightning may not penetrate 
the body if the person is wet. Then, 
most of the current descends 
through the water sheath on the 
body. (Wet trees struck by lightning 
may be completely unharmed. See 
FC 6.41.) In this case, the victim's 
breathing and heart may be 
stopped by the electrical shock, but 
quick application of artificial 
respiration can revive the person. 
Many times a lightning victim does 
not suffer a direct hit, but is hit by a 
side-splash from the object 
suffering the direct hit or is felled by 
the ground currents of the hit (FC 
6.45). One reference suggests that 
most people dying from lightning 
do so only because rescuers 
prematurely give them up for dead. 
Hence, common first aid for 
electric shock should always be 

given a lightning victim. 

6.48 See FC 6.46. 

6.49 The pin wheel does not 
move because of something 
thrown off or pulled on, but 
because of the ionization of the air 
next to the point. Once the air is 
ionized in the high electric field of 
those points, the ions and the point 
have the same sign of charge and 
thus repel each other. The 
ionization and consequent 
repulsion occurs regardless of 
whether the pinwheel is charged 
negatively or positively. 

6.50 The alternating high voltage 
induces an alternating current in 
nearby metal objects, which then 
may be discharged by an unwary 

person grounding part of the 

7.1 As fascinating as the 
possibility of communicating with 
an extraterrestrial civilization is, 
one should remain somewhat 
skeptical about the occasional 
flood of "flying saucer" 
sightings— at least skeptical 
enough to retain the fundamental 
physics man has developed. Many 
of the sightings would have to 
violate those basic laws if they 
were truly sightings of machines. 
The gravity shielding scheme is 
untenable. If, as in H. G. Wells' 
story, a ship could be shielded 
from the earth's gravity but still 
exposed to the moon's gravity, the 
resulting acceleration would be 
ridiculously small, about a millionth 
of the acceleration of a freely 
falling body near the earth's 
surface. Besides, there is 
absolutely no evidence for 
antigravity or gravity shielding, and 
such effects might even be 
theoretically inconsistent with 

292 Flying circus of physics with answers 

modern physics. 

7.3 Numerous arguments have 
been published to resolve the 

paradox, ranging from limiting the 
extent of the universe to a finite 
radius to red-shiftrng the light from 
very distant stars so severely that it 
is essentially nonexistent. [The 
red-shift is the Doppler shift of light 
from a source moving away from 
the observer and is similar to the 
Doppier shift in sound (FC 1.65).] 
Probably the best argument is a 
recent one (1587). The sky is not 
ablaze with light because a theory 
that assumes that all the stars in 
the universe are lit simultaneously 
must be wrong. The typical lifetime 
of a star can be taken as about 
10 10 years. Although this time 
seems very long, it is not when 
compared to the time about 10 24 
years necessary for the universe to 
reach thermodynamic equilibrium. 
"In other words, this means that the 
luminous emissions from stars are 
much too feeble to fill in their 
lifetime the vast empty spaces 
between stars with radiation of any 
significant amount" 

7.4 The nature of noctilucent 
clouds is still controversial, but 
they are probably due to the 
condensation and freezing of water 
on dust particles at the 
mesopause, which is a relatively 
low temperature region near the 
altitude of 90 km. The dust could 
be cosmic dust (star dust), comet 
dust thrown off during a comet's 
passage by the sun, or dust from 
the astroidal belt. The clouds can 
be seen only during sunset 
because they are so faint. They 
can be seen then only because 
they are so high that they are still 
illuminated by the setting sun when 
the ground observer has entered 

twilight. The wavy structure is due 
to the passage of atmospheric 
gravity waves, periodic variations 
in the density and temperature of 
the air. 

7.5 I have no answer to this 
question, and the literature is of no 
help in resolving the controversy. 
Experiments to show the statistical 
success of water witches is 
unconvincing and marginal and 
leaves the reader a believer only if 
he or she were already a believer. 
Unless someone publishes a very 
careful experiment in which the 
signal is clearly shown, water 
witching will remain controversial. 
For example, if the water witch 
subconsciously detects a very 
weak electromagnetic noise signal 
from running water, then that 
signal will have to be detectable on 
sensitive instruments and then 
correlated with the water witch's 

7.6 The snow waves are 
probably the progressive lowering 
of snow that lays over a structurally 
weak layer of hoarfrost, a situation 
that is also responsible for some 
avalanches (FC 3.47), 

7.8 The original, purely 
tongue-in-cheek calculations by 
David Stone (1424) indicated that 
such a jump by the Chinese would 
produce an earthquake with a 
Richter scale magnitude of 4.5. 
The jump would surely devastate 
part of China. But if the ground 
wave is resonantly amplified, 
destruction elsewhere would also 
be possible. To make resonance, 
the Chinese would have to jump 
every 53 or 54 min, the time a 
ground wave requires to circle the 
earth. To protect itself, the target 
nation would have to organize 
jumps whose waves would cancel 

the Chinese-generated waves. 
Since the target nation would have 
a smaller population, the jumps 
would have to be from 
proportionally greater heights. One 
writer to Time magazine argued 
that any jumps must be with stiff 
knees in order to impart the 
greatest energy to the waves. The 
difference between still- and 
loose-kneed jumping is not clear to 
me. since the energy imparted 
must be the gravitational potential 
energy in both cases. But were his 
argument correct, he points out 
that a resonant wave "would not be 
generated . . . because the only 
weapon derived from the actions 
would be the ear-shattering 
scream from 750 million badly 
maimed Chinese" (1425). 

7.9 The protein molecules in the 
egg white are initially in a 
spaghetti like mess. Beating or 
heating the egg whites untangles 
those long molecules, and they 
then can attract each other 
sufficiently to give a firmer 

7.10 Apparently no complete 
explanation for the compression 
point has been published, although 
one could guess that it is caused 
by the flow of the adhesive layer 
beneath the tape toward the 
separation point. 

7.11 through 7.13 These three 
phenomena are really the same. Til 
explain the first one and leave the 
other two for you. Osborne 
Reynolds explained the whitening 
of beach sand in 1885 when he 
pointed out that the sand 
expanded when stepped on. Prior 
to the pressure, the sand grains 
were as closely packed as 
possible. Under the shearing from 
the footstep, the disturbance to the 

Answers 293 

grains could only result in less 
efficient packing. In other words, 
the sand was forced to occupy 
more volume because of the 
shearing. Whereas the sand level 
suddenly rose, the water level 
could change only through 
capillary action, and that took 
some time. Thus, just after the 
footstep, the sand beneath the foot 
had risen above the water and 
was, for a little while, dry and white. 

7.14 Recent publications 
indicate that the radiation level in 
high altitude jets is not of much 
concern. Radiation from the sun 
occurs principally during solar 
flares, and those are being 
monitored. The more serious 
danger was thought to lie in the 
heavy nuclei from our galaxy that 
could produce 1000 rads near the 
end of their trajectory if they stop in 
human flesh. This rate should be 
compared with the limit of 100 rads 
per week for radiation workers. 
However, the heavy nuclei flux at 
the flight altitudes is only a few 
percent of that in space and is 
thought not to be a serious 
problem after all. (Improperly 
shielded astronauts will have more 
to worry about.) Although the 
primary cosmic particles are 
apparently safe for airplane 
passengers, still uncertain is the 
effect of the secondary neutrons, 
tow- energy protons, and alpha 
particles produced by the primary 

7.15 The flashes observed by 

astronauts and by researchers 
sitting in the beams of accelerated 
particles are likely produced by a 
variety of mechanisms. Either the 
cosmic ray particles or the 
man-made beams might be able to 
produce light by Cerenkov 

radiation in the eye, direct 
excitation of the retina, and 
fluorescence of the lens. 
(Cerenkov radiation is that 
radiation accompanying a particle 
whose velocity in a material 
exceeds the velocity of light in that 
material. The radiation forms a 
bow wave with the particle at the 
vertex, similar to the bow wave 
formed in the shock wave of a 
supersonic airplane.) Some of the 
light flashes are probably 
connected with the phosphenes 
discussed in FC 5.121. 

7.16 The ability of using X-ray, 

infrared, and ultraviolet light to 
expose multiple layers of paintings 
lies in the different responses of 
the different paints and other 
materials used in the paintings. For 
example, infrared analysis of "The 
Marriage of Arnolfini" by van Eyck 
exposed an original sketch of 
Arnolfini's right hand that was done 
in charcoal on the white chalk 
background. That sketch was 
buried beneath the final painting of 
the hand. In the infrared 
photograph the charcoaled hand 
appeared because it greatly 
absorbed the infrared whereas the 
white chalk did not; the hand thus 
appeared dark in the photograph. 
Under ultraviolet light, different 
paints fluoresce differently, and 
alterations to original paintings can 
be detected in a similar manner, 

7.17 Part of the energy from the 

particle and electromagnetic 
radiation emitted by the initial burst 
is absorbed by the air in the 
immediate vicinity of the burst. 
Those air molecules are highly 
excited or ionized, and the 
resulting deexcitation and 
recombination yields visible light. 
About half of the initial burst energy 

is released as mechanical energy 
(and develops a shock wave), 
about a third emerges as 
electromagnetic energy (infrared, 
visible, UV, X rays, and gamma 
rays) and the rest is given to 
particles. The shock wave rapidly 
compresses the air, heating it to 
incandescence. The temperature 
of the fireball's surface about 10- 4 
s after burst can be 3 x 10 5 K or 
greater. The fireball expands and 
cools, and eventually the shock 
wave breaks away from the ball 
and thus no longer causes 

7.18 Although Herbert did not 
have this in mind, there is an 
analogy in physics. If a metal plate 
is swung into a magnetic field, 
such as a metal pendulum swung 
between the pole faces of a 
horseshoe magnet, the kinetic 
energy of the plate is lost to Joule 
heating in the metal. This loss is 
due to the currents created in the 
plate by the change in the 
magnetic field experienced by the 
plate swinging through the magnet. 
For example, the field first 
increases as the plate nears the 
pole faces, and then decreases as 
the plate swings away. The 
currents created in the plate heat 
the plate in the same way that 
electric currents heat the coils in an 
electric oven. The original kinetic 
energy of the moving plate is 
eventually dissipated as this 
heating, and the plate stops. 

7.19 Modem work on friction 
discredits the old theory about it 
originating entirely from surface 
irregularities and instead points to 
the adhesion between the surfaces 
(due to molecular attraction) as 
being the main cause of friction. In 
spite of this work, many physics 

294 Flying circus off physics with answers 

textbooks stiJI regard friction as 
being due only to hills and valleys 
in the surfaces jamming together. 

7.20 Pure lead is soft; it can be 
cut with a fingernail, When the 
Cathedral's roof heated during a 
Washington summer day, it might 
have reached temperatures near 
80°C, high enough that the lead 
became malleable enough to flow 
under its own weight. Less pure 
lead would be less malleable, and 
the roof was remade with an alloy 
of 94% lead and 6% antimony. The 
European structures did not have 
such a problem because their lead 
was un pure to begin with and 
because their summer days were 
not as hot 

7.21 Cracks begin at small, 
perhaps invisible defects that form 
when the material is first fabricated 
or that develop later under the 
wear and tear of use. These cracks 
greatly weaken the material 
structure, because they 
concentrate an applied force on 
the vertex of the crack. Such 
concentration means that a force 
normally too small to rip the 
material apart if there were no 
cracks, can now propagate the 
crack through the object. Some 
cracks expand because of 
corrosion. Foreign molecules may 
enter the crack, break the bonding 
of the material's molecules at the 
crack's vertex, and then react with 
these molecules. If the resulting 
new molecular structure occupies 
more volume than the original 
structure, the new structure pries 
the crack open, 

7.22 The corrosion begins when 
electrons released by the wet nickel 
tunnel through the oxide layer on 
the chromium surface to reach an 

oxygen species. As a result the 
nickel is slowly dissolved at the 
defect site. But the rate of the 
reactions is controlled by the 
electron flow. If only a few defects 
are in the bumper, the electrons 
come from only those few places, 
the nickel there is relatively quickly 
dissolved, and the iron layer is soon 
exposed and becomes rusty. If 
there are many (small) defects, 
then fewer electrons come from 
each, and the dissolving of the 
nickel and exposing and rusting of 
the iron at each defect are much 
slower, giving a longer life to the 

7.23 The process of polishing a 
surface does not depend on 
transferring material from the hills 
to the valleys on the surface or on 
heating the surface. The first does 
not occur, and the latter may be 
undesirable if the surface is 
sufficiently heated as to develop 
waves. Polishing removes material 
from the hills on the surface. Under 
a heavy load, larger pieces of 
material are removed; under a light 
load, individual molecules are 
removed. Eventually the hills are 
worn down to the level of the 
valleys, and the surface is then 
smooth on a microscopic level. 

7.24 Adhesives are adhesive 
because of molecular attraction 
between the surfaces of the 
adhesive and of the material to 
which it is applied. Any material 
could be an adhesive, although 
most are not useful because of 
their other properties. For 
example, liquid water could glue 
things together were it not for its 
low shear strength. Most 
adhesives are liquid, at least 
initially, because of the need for 

close contact between the glue 
and the materials being glued. In 
order for two surfaces to adhere, 
they must be within a few 
angstroms of each other. (An 
angstrom is 10- 10 m, about the 
size of small atoms and 
molecules.) Most solid surfaces 
are too rough to allow more than a 
tiny amount of their surface area to 
be this close, A liquid glue can flow 
into those surface irregularities and 
thus provide the close contact 
Another reason most surfaces, 
such as the broken edges of my 
coffee cup, do not adhere on 
contact is that they are dirty. Were 
they both clean and smooth, the 
surfaces might spontaneously 
adhere, as was feared in the early 
space missions. Such 
spontaneous adhesion can be 
observed in freshly separated 
layers of mica. If you rejoin the 
surfaces a few seconds after 
separation, the layers adhere. 
However, if you wait for several 
minutes, the air and its dust will 
contaminate the exposed surfaces 
to prevent any such adhesion. 

Answers 295 

Jeer! Walker 

This original offbeat booh is a collection of problems and 
questions about physics in the real everyday world. 
The questions focus an relevant, fun phenomena— like 
Frisbees, sounds of thunder, rainbows, sand dunes, soap 
bubbles. And they involve familiar objects considered in 
imaginative, unconventional ways— rubber bands, ski 
goggles, water pipes, eggs, teapots. Coke bottles. 

It's a new way to learn, to appreciate basic science by thinking 
about questions you may not have thought of! 







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